forked from 1b-agent/fieldcraft-upstream
verification: implicit contact patch test and Hertz line contact
Two oracle cases: the contact patch test on non-matching meshes in small and finite sliding, and Hertz's cylinder on a flat under force control (peak pressure, pressure distribution, subsurface stress). docs/fem.md describes the formulation, the literature survey its papers; ROADMAP M7 and parity are updated. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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@@ -33,7 +33,7 @@ pressure) is a degree of freedom of the existing DOF framework, not a separate s
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| M4 Own solver and first results | Element library per docs/elements.md (1D and 2D first); Linear static and modal solver (tet4/10, wedge6, hex8, hex20; sparse direct, Lanczos), verified against analytic solutions (solver: done — `fieldcraft-fem` kernels, `fieldcraft-solver` with nested dissection, sparse Cholesky and block Lanczos, `solve.static`/`solve.frequency`/`solve.probe`, patch, cantilever, Lamé, Kirsch and beam-frequency tests; reference points with kinematic and distributing couplings and moments by master–slave constraint elimination, verified by rigid motion, clamping, Saint-Venant tension, bending and tube torsion; 1D elements I: rod2/rod3 trusses, point masses, rotary inertia, springs and dashpots in both solvers and all three decks, verified by the method of joints, the three-bar truss, spring–mass, two-mass chain and torsional pendulum frequencies, and damped decay; 2D elements: plane stress, plane strain and axisymmetric tri3, tri6, quad4 (incompatible modes QM6), quad8 with two degrees of freedom per node, centrifugal loads, `mesh.planar` 2D meshes of polygons and planar faces, verified by patch tests, Kirsch, Lamé (plane strain and axisymmetric), rotating discs and cylinders, and a plane stress cantilever; deck mapping to Abaqus CPS/CPE/CAX, Nastran membranes, LS-DYNA ELFORM 12/13); shells and beams (done: quad4 MITC4 and tri3 MITC3 flat shells with a Hughes–Brezzi drilling rotation, two-node Timoshenko beams with profile properties and orientations, six degrees of freedom at shell and beam nodes shared with solids and trusses, section forces and surface stresses, verified by shell patch tests, Navier's plate, cantilever and portal-frame beams, and the Scordelis–Lo and pinched-cylinder benchmarks); results display (done: `results.*` commands, deformed shape to scale, banded contours of displacement, von Mises, principal and component stresses with a legend, mode shapes with their frequencies and animation, probing a node by clicking it, reaction force and moment sums per set, stale results marked after an edit; explicit steps: field frames by slider or animation with contours per frame, energy histories plotted) | started |
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| M5 Structured hex | 2D quad meshing of faces (`fieldcraft-mesh::quad`: transfinite mapped meshes, free all-quad meshes of polygons with holes on prescribed boundary nodes, exact planar quad validity, shared `SizeField` and even edge divisions; done for planar faces); mapped hex of six-sided regions (trivariate TFI, curved faces) and sweep meshing (multi-level extrusions with imprinted cross-sections, revolutions, one-to-one sweeps through linking faces; interval assignment, hex8/hex20 on the geometry, B-rep face tags, `mesh.hex.generate`/`sweep`/`mapped`: done, 16 of 21 corpus parts all-hex); conforming interfaces between cells (done: `mesh.hex.blocks` meshes a part split with SolidCraft's Split Body into mapped blocks as one conforming mesh — composite faces for seams and tangent faces, interval assignment over all cells, shared faces meshed once, grading off holes and fillets, free-internal-face check; the filleted bracket in 30 cells, hex20 within 0.1 % of a fine tet10 tip deflection); sweepable cells in a conforming mesh and tet–hex transition; automatic decomposition into sweepable and mappable regions, proposed as SolidCraft splits | started |
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| M6 Automatic hex | Octree/grid all-hex for any part (first version: done — `fieldcraft-mesh::octree`, `mesh.hex.octree`: 3-refinement grid with conforming templates refined by curvature, thickness and narrow faces, a core cleared to a manifold boundary, feature map onto it, padding and a pillow per patch capturing every sharp curve, foldover-free fitting, certified validity, B-rep face tags; the corpus hex column and the filleted-bracket oracle case; next: transitions for concave refined regions so thin and curved parts stop over-refining); hex-dominant by tet recombination; polycube for blocky parts; layers through thin walls; mesh editing and orphan-mesh import | started |
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| M7 Assemblies, contact and friction | Needs M15. Part instances from SolidCraft occurrences; tie between non-matching meshes (mortar); implicit contact: surface-to-surface mortar and node-to-surface, penalty and augmented Lagrange, self-contact, automatic pair detection (the model's contact definitions, `interaction.contact.*` with `find`, the deck mapping, `fieldcraft_fem::contact`'s closest-point projection and bucket grid, and the explicit solver's segmentation and friction return map are in place to reuse; the implicit solver refuses contact by name until then); friction: Coulomb with stick–slip, static/kinetic, anisotropic, pressure-, rate- and temperature-dependent coefficients; contact output (pressure, slip, status); thermal contact conductance and frictional heating; wear (Archard); bolt pretension, connectors with behaviour (elastic, damped, stops, locks); amplitudes, multiple steps, restart; nonlinear steps in all three decks. Verified by Hertz (sphere and cylinder), the Cattaneo–Mindlin partial-slip problem, the sliding block, NAFEMS contact benchmarks | planned |
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| M7 Assemblies, contact and friction | Needs M15. Part instances from SolidCraft occurrences; tie between non-matching meshes (mortar); implicit contact: surface-to-surface mortar and node-to-surface, penalty and augmented Lagrange, self-contact, automatic pair detection (frictionless mortar contact pairs in nonlinear static steps: done — segment-to-segment mortar with the consistent tangent by automatic differentiation of the segmentation, augmented Lagrangian with Uzawa updates to a gap tolerance, semismooth active set with a chattering cutback, small sliding without nonlinear geometry and finite sliding with it, overclosure adjusted or refused, pressure, gap and status output; verified by the contact patch test, Hertz cylinder and sphere and Newton's quadratic rate; the linear analyses refuse contact by name); friction: Coulomb with stick–slip, static/kinetic, anisotropic, pressure-, rate- and temperature-dependent coefficients; contact output (pressure, slip, status); thermal contact conductance and frictional heating; wear (Archard); bolt pretension, connectors with behaviour (elastic, damped, stops, locks); amplitudes, multiple steps, restart; nonlinear steps in all three decks. Verified by Hertz (sphere and cylinder), the Cattaneo–Mindlin partial-slip problem, the sliding block, NAFEMS contact benchmarks | started |
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| M8 Materials, explicit, shells, composites | Plasticity, hyperelasticity, damage data per solver; explicit dynamics decks (Abaqus/Explicit, LS-DYNA); midsurface shells; composite layups and material orientations, continuum shells on swept hex; hybrid (mixed u–p) hex8/hex20/tet10 for nearly incompressible materials (done); heat transfer (solids done: steady and θ-method transient conduction with flux, convection and sources, thermal strain in static steps (solids and 2D) and explicit dynamics (with plasticity), coupled temperature–displacement, `solve.heat`; deck output, 2D/shell/beam conduction planned) | started |
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| M9 Post-processing and deck readers | Results readers for public formats (Nastran OP2, LS-DYNA d3plot, Abaqus `.fil`); XY and path plots, cuts, display groups, free-body forces; deck readers that keep unknown keywords; mesh convergence studies | planned |
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| M10 Explicit dynamics | Shared element and material kernels with the implicit solver (`fem`); central-difference solver with lumped mass, stable time step, one-point hex8 with hourglass control and nodal-pressure tet4, bulk viscosity, energy accounting (X1 core: done — `fieldcraft-explicit`, `explicit_dynamic` steps with initial velocities, prescribed motion and planar rigid walls, `solve.explicit`/`solve.history`, small-strain linear elastic; bar wave, rigid-wall impact, energy balance and cantilever-period tests); large-deformation materials (X2: done — updated Lagrangian elements, Jaumann/Hughes–Winget and Green–Naghdi/Flanagan–Taylor rates, J2 bilinear/table plasticity, Johnson–Cook strength with heating and damage, erosion; materials gain `plastic`, `damage`, `erosion` with `model.material.plasticity`/`damage`; Dienes shear, rigid rotation, J2 uniaxial and Taylor-bar tests); contact (X3: done — `interaction.contact.pair`/`general`/`find`, segment-to-segment penalty contact both ways with polygon clipping (passes the contact patch test on non-matching meshes), pairs, general (all exterior faces) and self contact, bucket-grid search, deterministic on any thread count, a penalty from the masses and the stable increment that never shortens it, Coulomb friction with exponential decay by a return map, friction on rigid walls, contact energy and friction dissipation in the balance, initial penetrations adjusted or refused; Abaqus `*CONTACT PAIR`/`*CONTACT`/`*FRICTION` and LS-DYNA automatic contacts in the decks; verified by colliding bars, sliding blocks, the patch test and Hertz's sphere impact); hyperelastic materials (neo-Hookean, Mooney–Rivlin, Yeoh) on the shared material point with average nodal pressure tets, and opt-in mass scaling with the added mass reported: done; runs on hex and tet meshes | started |
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@@ -77,7 +77,7 @@ What exists and what is missing, by area; each gap is in a milestone above.
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| Area | Today | Missing |
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|---|---|---|
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| Solution procedures | Linear static, nonlinear static (solids with geometric and material nonlinearity: hyperelasticity, J2 plasticity), frequency (Lanczos), steady and transient heat, coupled temperature–displacement, explicit dynamics, LBM flow | Nonlinear shells and beams, arc-length, buckling (M15); implicit, harmonic, random and spectrum dynamics (M16) |
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| Contact, friction, adhesion | Explicit deformable contact (pairs, general, self; segment to segment, penalty) with Coulomb friction and exponential decay; rigid walls with friction; couplings, springs, dashpots | Implicit contact, tie, anisotropic and pressure- or temperature-dependent friction, thermal contact, wear, eroding contact (M7, M10); cohesive adhesion and debonding (M20) |
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| Contact, friction, adhesion | Explicit deformable contact (pairs, general, self; segment to segment, penalty) with Coulomb friction and exponential decay; rigid walls with friction; implicit mortar contact pairs (frictionless, augmented Lagrangian) in nonlinear static steps; couplings, springs, dashpots | Implicit friction and self contact, tie, anisotropic and pressure- or temperature-dependent friction, thermal contact, wear, eroding contact (M7, M10); cohesive adhesion and debonding (M20) |
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| Materials | Isotropic and orthotropic elasticity, density, thermal, J2 plasticity (bilinear, table, Johnson–Cook), Johnson–Cook damage and erosion, compressible neo-Hookean, Mooney–Rivlin and Yeoh hyperelasticity, Newtonian fluids | Elastomers beyond Yeoh (Ogden, Arruda–Boyce and the rest), viscoelasticity, viscoplasticity and creep, anisotropic and pressure-dependent plasticity, non-Newtonian viscosity, a cited material library and calibration (M17) |
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| Composites and anisotropy | Orthotropic constants | Orientations, layups, ply results, failure criteria, homogenisation (M18) |
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| Coupled fields | Thermal–structural (one way and coupled) | Piezoelectric, poroelastic, electro-thermal, acoustics (M19) |
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@@ -408,7 +408,8 @@ analysis stops naming the node, the face and the depth). Planar rigid walls take
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Commands `interaction.contact.pair|general|edit|delete|find`; Abaqus writes `*SURFACE
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INTERACTION` with `*FRICTION` (exponential decay), `*CONTACT PAIR` and general `*CONTACT`, LS-DYNA
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`*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE` and `_SINGLE_SURFACE` (`fs`, `fd`, `dc`, `sfsa`,
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`sfsb`); Nastran and the implicit solver refuse contact by name (implicit contact is M7).
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`sfsb`); Nastran and the linear implicit analyses refuse contact by name; nonlinear static steps
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take contact pairs (next section).
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**Geometry** (`fieldcraft_fem::contact`, shared with the implicit solver to come): the closest
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point of a triangle (exact region tests) or of a bilinear quadrilateral (projected Newton with the
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@@ -451,6 +452,76 @@ Hertz (peak force +2.3%, duration −0.4% on a graded quarter-sphere mesh), a fr
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by general contact on all its faces, initial penetrations adjusted or refused, the face cap, and
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bit-for-bit results on one and four threads.
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## Contact in nonlinear static steps (mortar, augmented Lagrangian)
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**Discretisation** (`fieldcraft_solver::contact`): mortar contact, one pass, the pair's
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`secondary` surface the non-mortar side. Each secondary node A carries a pressure p_A and the
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weighted gap g̃_A = Σ ∫ Φ_A (x_m − x_s)·n dA over the overlaps of its faces with the main faces
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facing them, Φ_A the secondary face's own shape functions; ĝ_A = g̃_A / A_A with A_A = ∫ Φ_A over
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the node's faces. The pressure field is interpolated like the displacements, so a uniform
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pressure crosses a non-matching interface as the consistent nodal forces of both meshes: the
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contact patch test. Linear faces (tri3, quad4: tet4, wedge6, hex8); general contact, quadratic
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faces, 2D models and arc-length steps are refused by name.
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**Segmentation** (`fieldcraft_fem::mortar`): both faces are projected along the secondary
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face's unit normal onto its plane, the main polygon is clipped by the secondary one
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(Sutherland–Hodgman; a projected quadrilateral that is not convex goes as its two triangles), and
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the overlap's fan of triangles is integrated with Radon's seven-point degree-5 rule. At each point
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both faces' coordinates come from inverting their projected maps (linear, or bilinear by the root
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of its quadratic), so the main point is on the main surface along the normal, warped or not. A
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vertex within 10⁻⁸ of a clip edge's length of its line is on it and never cut: the intersection
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of two nearly coincident edges is ill-conditioned and its derivative swamped by round-off. The
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kernel is written over a generic scalar: `f64` for values, forward-mode `Dual` for gradients and
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`Hyper` (gradient and packed Hessian in the 24 corner coordinates) for the consistent tangent,
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the exact linearisation of the segmentation, normal and projection (`fieldcraft_fem::dual`).
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**Enforcement**: augmented Lagrangian. With the multipliers λ_A fixed, p_A = ⟨λ_A − ε_A ĝ_A⟩,
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the derivative of Π = Σ A_A/(2ε_A) ⟨λ_A − ε_A ĝ_A⟩²: internal forces −p_A ∂g̃_A/∂x and the tangent
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Σ_closed (ε_A/A_A) ∂g̃_A ⊗ ∂g̃_A − p_A ∂²g̃_A (the second term the contact's geometric stiffness).
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Once Newton converges an increment, λ_A ← p_A (Uzawa) and the increment is solved again from its
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solution, until every closed node's gap is within 10⁻⁵ of the thickness of the element under it
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and no open node keeps a multiplier (at most 25 augmentations, then a warning). The penalty per
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length is ε_A = s · 10 · 3Ḡ/h (Ḡ the mean shear modulus, h = V/A of the element under the face,
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s the contact's `penalty_scale`): about ten times the local element stiffness, and 3Ḡ rather than
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the constrained modulus keeps it so for nearly incompressible rubber.
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**Active set and Newton**: the max() decides at every evaluation which nodes are closed
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(semismooth Newton); an increment whose active set alternates between two states three times is
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cut back (chattering). The tangent's pattern takes the blocks of the closed nodes' face pairs on
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top of the mesh's. With contact, the force scale of the convergence test is that of the
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converged states, the loads and the current state rather than the largest force of every trial
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(a trial can press a body deep into another before the active set settles). The augmentations'
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re-solutions are measured against the increment's start and its first correction; the next
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increment's size follows the increment's own iterations.
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**Small and finite sliding**: without nonlinear geometry the face pairs (those within a main
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element's thickness) and their mortar integrals D_ai = ∫ Φ_a N_i, M_aj = ∫ Φ_a N_j are fixed in the
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reference configuration, so g̃_a = n · (Σ M_aj x_j − Σ D_ai x_i) is linear: exact and quadratic-free.
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With nonlinear geometry the pairs are searched (bucket grid of the main faces' boxes grown by
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their depth limit) and integrated on the current configuration at every evaluation; a pair deeper
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than half the main element's thickness has passed through and is left out.
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**Initial overclosure**: nodes whose gap starts negative are reported; `adjust` takes the overlap
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out of their weighted gap (an offset: strain-free, nodes are not moved), `refuse` stops naming
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the node and the depth.
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**Output**: per secondary node the pressure (its normal contact force over the area it carries,
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∫ Φ_A over the overlaps, which is smoother than the multipliers at the contact's edge), the
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multiplier, the gap ĝ and the status (open, closed); per contact the force on the secondary
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surface, the normal force Σ p_A ∫Φ_A, the deepest penetration and the augmentations.
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`solve.nonlinear` summarises each contact, `solve.probe` gives a secondary node's `contact`
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entries, and the results display draws `contact_pressure`, `contact_gap` and `contact_status`.
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**Verification** (`crates/solver/tests/contact.rs`, `tests/oracle/nl-contact-patch`,
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`tests/oracle/nl-hertz-cylinder`): the contact patch test on non-matching hex8 and tet4 meshes
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(uniform σ_zz, pressure equal to it, no lateral stress: to 10⁻⁹ with small sliding, 10⁻⁴ with
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finite sliding, where the gaps the augmentation leaves enter through their geometric terms);
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Hertz's line contact, plane strain (peak pressure within 0.3%, the pressure at two nodes within
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3% and 6%, the vertical stress under the contact within 2%, the half-width bracketed); Hertz's
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sphere on a flat, a quarter model (peak pressure within 4%, contact radius bracketed; heavy);
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Newton's quadratic rate near the solution with finite sliding; initial overclosure adjusted and
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refused; bit-for-bit results on one and four threads; the refusals.
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## Hyperelastic materials in explicit dynamics
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Hyperelastic materials (neo-Hookean, Mooney–Rivlin, Yeoh) use the shared finite-strain material
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Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the policy is [verification.md](verification.md). Every case is our own model, built with FieldCraft commands from the problem's published description, and compared with the reference value its `expected.json` cites, within the stated tolerance and for the stated reason. Accepted results are frozen in each case's `fixture.json`: a later change that moves one beyond its band (10⁻⁹ of its size) fails CI even while the reference still passes. No reference value was produced with a commercial product.
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**201 of 207 quantities pass** (6 known failure(s)) in 62 active cases: 53 theory, 9 published benchmark, 0 experiment; 10 pending cases wait for capabilities still being built.
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**222 of 228 quantities pass** (6 known failure(s)) in 64 active cases: 55 theory, 9 published benchmark, 0 experiment; 10 pending cases wait for capabilities still being built.
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## Theory: closed-form solutions, patch tests and mesh invariants
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@@ -80,6 +80,21 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
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| [lame-cylinder-plane-strain](../tests/oracle/lame-cylinder-plane-strain/) | radial displacement at the bore (10, 0) | 0.0090794 | 0.0090793 | -0.000267% | 0.1% | pass | matches |
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| [lame-cylinder-plane-strain](../tests/oracle/lame-cylinder-plane-strain/) | hoop stress σ_θ = σ_yy at the bore (10, 0) | 166.67 | 166.36 | -0.183% | 1% | pass | matches |
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| [lame-cylinder-plane-strain](../tests/oracle/lame-cylinder-plane-strain/) | axial stress σ_zz = 2νA at the bore (plane strain) | 20 | 20.083 | 0.415% | 1% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: σ_zz of the lower block's corner element under the interface (element 10) over that of the upper block's corner element over it (element 19) | 1 | 1 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: σ_zz of the lower block's centre element under the interface (element 14) over that of element 19 | 1 | 1 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: σ_zz of the lower block's bottom corner element (element 1) over that of element 19 | 1 | 1 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: σ_zz of the upper block's top far corner element (element 26) over that of element 19 | 1 | 1 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: σ_xx of element 14 over its σ_zz (uniaxial stress: 0) | 0 | ≈ 0 | ≈ 0 | ± 1.0000e-6 | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: the contact pressure at the secondary node (0.5, 0.5, 1) over −σ_zz of element 19 | 1 | 1 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: the integrated contact pressure over the reaction at the pushed top | 1 | 1 | < 1e-7% | 1e-6 rel. | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: σ_zz of the lower block's corner element under the interface (element 10) over that of the upper block's corner element over it (element 19) | 1 | 1 | 0.000151% | 0.02% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: σ_zz of the lower block's centre element under the interface (element 14) over that of element 19 | 1 | 0.99999 | -0.00129% | 0.02% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: σ_zz of the lower block's bottom corner element (element 1) over that of element 19 | 1 | 0.99999 | -0.000942% | 0.02% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: σ_zz of the upper block's top far corner element (element 26) over that of element 19 | 1 | 0.99999 | -0.000872% | 0.02% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: σ_xx of element 14 over its σ_zz (uniaxial stress: 0) | 0 | ≈ 0 | ≈ 0 | ± 2.0000e-4 | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: the contact pressure at the secondary node (0.5, 0.5, 1) over −σ_zz of element 19 | 1 | 0.99998 | -0.00172% | 0.02% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Finite: the integrated contact pressure over the reaction at the pushed top | 1 | 1 | < 1e-7% | 0.02% | pass | matches |
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| [nl-contact-patch](../tests/oracle/nl-contact-patch/) | Small: σ_zz of element 19 (uniaxial stress E ε = −10 for the 1% squeeze) | -10 | -9.9996 | 0.00426% | 0.01% | pass | matches |
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| [nl-cylinder-inflation](../tests/oracle/nl-cylinder-inflation/) | radial displacement of the bore (10, 0, 0) at the pressure that inflates it to a = 15 | 5 | 5.004 | 0.0793% | 0.5% | pass | matches |
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| [nl-cylinder-inflation](../tests/oracle/nl-cylinder-inflation/) | radial displacement of the outer wall (20, 0, 0) | 2.9129 | 2.9173 | 0.152% | 0.5% | pass | matches |
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| [nl-elastica-cantilever](../tests/oracle/nl-elastica-cantilever/) | tip deflection δ_v/L at P L²/(E I) = 1 | 0.30172 | 0.30226 | 0.179% | 1% | pass | matches |
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@@ -90,6 +105,12 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
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| [nl-elastica-cantilever](../tests/oracle/nl-elastica-cantilever/) | tip shortening δ_h/L at P L²/(E I) = 5 | 0.38763 | 0.38955 | 0.495% | 2% | pass | matches |
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| [nl-elastica-cantilever](../tests/oracle/nl-elastica-cantilever/) | tip deflection δ_v/L at P L²/(E I) = 10 | 0.81061 | 0.81421 | 0.444% | 1% | pass | matches |
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| [nl-elastica-cantilever](../tests/oracle/nl-elastica-cantilever/) | tip shortening δ_h/L at P L²/(E I) = 10 | 0.555 | 0.558 | 0.541% | 2% | pass | matches |
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| [nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/) | the largest contact pressure p₀ (at x = 0) | 2884.6 | 2892 | 0.254% | 2% | pass | matches |
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| [nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/) | the force across the contact (half model, 1 mm thick) | 1132.8 | 1133 | 0.0221% | 0.2% | pass | matches |
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| [nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/) | the contact pressure at the secondary node at x = 0.29594 (node 7) | 2325.1 | 2257.8 | -2.89% | 5% | pass | matches |
|
||||
| [nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/) | the contact pressure at the secondary node at x = 0.36701 (node 8) | 1959 | 2078.4 | 6.09% | 10% | pass | matches |
|
||||
| [nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/) | the contact pressure at the secondary node at x = 0.63325 (node 11, beyond the half-width b = 0.5) | 0 | ≈ 0 | ≈ 0 | ± 1 | pass | matches |
|
||||
| [nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/) | the vertical stress σ_yy under the centre of contact at depth 0.47127 (node 713) | -2099.2 | -2059.8 | 1.87% | 4% | pass | matches |
|
||||
| [nl-hybrid-incompressible](../tests/oracle/nl-hybrid-incompressible/) | axial Cauchy stress, stretch λ = 2, ν = 0.4999 | 3.4988 | 3.4988 | 0.000000135% | 1e-6 rel. | pass | matches |
|
||||
| [nl-hybrid-incompressible](../tests/oracle/nl-hybrid-incompressible/) | lateral displacement at (1, 1, 1): l − 1 | -0.29281 | -0.29281 | < 1e-7% | 1e-6 rel. | pass | matches |
|
||||
| [nl-j2-uniaxial](../tests/oracle/nl-j2-uniaxial/) | axial Cauchy stress at a logarithmic strain of 0.2 | 642.74 | 642.74 | < 1e-7% | 1e-6 rel. | pass | matches |
|
||||
@@ -259,8 +280,10 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
|
||||
- **[nafems-le1](../tests/oracle/nafems-le1/)** (benchmark): NAFEMS LE1 elliptic membrane (hex20 plane stress layer). Source: NAFEMS, The Standard NAFEMS Benchmarks, TNSB Rev. 3, October 1990, test LE1 (target σ_yy = 92.7 MPa at D); as reproduced in the Abaqus 2017 Benchmarks Guide, 'LE1: Plane stress elements—elliptic membrane'. Tolerances — syy_D: the target is published to three figures; plane stress modelled by a thin solid layer and the stress extrapolated to the edge add a few tenths of a percent
|
||||
- **[nafems-le1-plane-stress](../tests/oracle/nafems-le1-plane-stress/)** (benchmark): NAFEMS LE1 elliptic membrane with 2D plane stress elements (quad8). Source: NAFEMS, The Standard NAFEMS Benchmarks, TNSB Rev. 3, October 1990, test LE1 (target σ_yy = 92.7 MPa at D); as reproduced in the Abaqus 2017 Benchmarks Guide, 'LE1: Plane stress elements—elliptic membrane'. Tolerances — syy_D: the target is published to three figures; the stress extrapolated to the edge on a converged mesh adds a few tenths of a percent
|
||||
- **[nafems-le10](../tests/oracle/nafems-le10/)** (benchmark): NAFEMS LE10 thick plate under pressure (hex20). Source: NAFEMS, The Standard NAFEMS Benchmarks, TNSB Rev. 3, October 1990, test LE10 (target σ_yy = −5.38 MPa at D); as reproduced in the Abaqus 2017 Benchmarks Guide, 'LE10: Thick plate under pressure'. Tolerances — syy_D: the target is published to three figures; at D the stress is extrapolated to a corner where the hole edge meets the loaded face, and published converged solutions scatter by 1–2% (Abaqus Benchmarks Guide fine meshes: −5.51 to −5.89)
|
||||
- **[nl-contact-patch](../tests/oracle/nl-contact-patch/)** (theory): Contact patch test: two blocks with non-matching meshes in uniaxial compression (implicit mortar contact). Source: The contact patch test: a contact discretisation must transmit a uniform pressure across a non-matching interface exactly; Taylor & Papadopoulos, On a patch test for contact problems in two dimensions, Nonlinear Computational Mechanics, Springer 1991, 690–702; Crisfield, Re-visiting the contact patch test, IJNME 48:435–449, 2000; passed by mortar methods: Puso & Laursen, CMAME 193:601–629, 2004. Uniaxial stress between frictionless symmetry planes is uniform in both blocks. Tolerances — small_lower_corner: small sliding is linear and its mortar integrals exact on these rectangular faces: a uniform stress is the discrete solution up to the convergence tolerance (10⁻¹⁰); small_lower_centre: as for the corner element; small_lower_base: as for the corner element; small_upper_top: as for the corner element; small_lateral: frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them; small_pressure: the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface; small_force: the pressure carries the whole load across the interface; finite_lower_corner: finite sliding is exact up to the geometric terms of the gaps the augmentation leaves (10⁻⁵ of the element thickness) and the default convergence tolerances; finite_lower_centre: as for the corner element; finite_lower_base: as for the corner element; finite_upper_top: as for the corner element; finite_lateral: frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them; finite_pressure: the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface; finite_force: the pressure carries the whole load across the interface; small_stress: the squeeze less the penetration the augmented Lagrangian leaves (up to 10⁻⁵ of the element thickness, a few 10⁻⁵ of the squeeze)
|
||||
- **[nl-cylinder-inflation](../tests/oracle/nl-cylinder-inflation/)** (theory): Inflation of a thick neo-Hookean cylinder by a follower pressure (plane strain). Source: Finite inflation of an incompressible neo-Hookean thick-walled tube in plane strain: r² = R² + a² − A², σ_θ − σ_r = μ (λ² − λ⁻²) with λ = r/R, integrated through the wall: p = (μ/2)[(ln λ_a² − λ_a⁻²) − (ln λ_b² − λ_b⁻²)] (R. S. Rivlin, Large elastic deformations of isotropic materials VI, Phil. Trans. R. Soc. A 242:173–195, 1949; R. W. Ogden, Non-Linear Elastic Deformations, Dover 1997, §5.3.2). Tolerances — ua: the closed form is incompressible and our material nearly so (κ/μ = 1000, a volume change of order p/κ ≈ 4·10⁻⁴); hybrid hex20, 6 × 16, follow the wall's strain gradient well inside; ub: as at the bore
|
||||
- **[nl-elastica-cantilever](../tests/oracle/nl-elastica-cantilever/)** (theory): Large-deflection cantilever under a dead tip load against the elastica (solids). Source: The elastica of a cantilever under a vertical end load: K. E. Bisshopp, D. C. Drucker, Large deflection of cantilever beams, Quarterly of Applied Mathematics 3(3):272–275, 1945 (elliptic-integral solution); values computed by integrating θ″ = −(P/EI) cos θ by shooting (our own RK4, 20000 steps), agreeing with the table of K. Mattiasson, Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals, IJNME 17(1):145–153, 1981, to all six digits. Tolerances — v1: hex20, 40 × 2 through the depth, L/h = 20: shear deformation (0.6 (h/L)² ≈ 0.15 % of the deflection) and the clamp's local restraint, both absent from the elastica; u1: as δ_v; the shortening is the smaller, second-order quantity, so its relative error is about twice the deflection's; v2: hex20, 40 × 2 through the depth, L/h = 20: shear deformation (0.6 (h/L)² ≈ 0.15 % of the deflection) and the clamp's local restraint, both absent from the elastica; u2: as δ_v; the shortening is the smaller, second-order quantity, so its relative error is about twice the deflection's; v5: hex20, 40 × 2 through the depth, L/h = 20: shear deformation (0.6 (h/L)² ≈ 0.15 % of the deflection) and the clamp's local restraint, both absent from the elastica; u5: as δ_v; the shortening is the smaller, second-order quantity, so its relative error is about twice the deflection's; v10: hex20, 40 × 2 through the depth, L/h = 20: shear deformation (0.6 (h/L)² ≈ 0.15 % of the deflection) and the clamp's local restraint, both absent from the elastica; u10: as δ_v; the shortening is the smaller, second-order quantity, so its relative error is about twice the deflection's
|
||||
- **[nl-hertz-cylinder](../tests/oracle/nl-hertz-cylinder/)** (theory): Hertz line contact: a cylinder pressed on a flat (implicit mortar contact, plane strain). Source: H. Hertz, Über die Berührung fester elastischer Körper, J. reine angew. Math. 92:156–171, 1882; K. L. Johnson, Contact Mechanics, Cambridge University Press 1985, §4.3 (two-dimensional contact of cylindrical bodies, eqs. 4.45–4.49): b = √(4PR/(πE*)), p₀ = 2P/(πb), with 1/E* = 2(1 − ν²)/E for two bodies of one material and R the cylinder's radius on a flat. Tolerances — peak_pressure: p₀ = 2P/(πb) for the load per length P = 2265.57 N/mm, b = 0.5 mm; the contact width spans seven elements of the graded mesh; normal_force: the pressure carries the whole load; the soft springs that hold the indenter before contact take a millionth; pressure_x0296: p₀ √(1 − x²/b²) at the node; the nodal pressure (the node's normal force over the area it carries) averages the distribution over the node's elements; pressure_x0367: as at node 7, nearer the edge, where the elements round off the square-root fall of the pressure to zero at b; pressure_x0633: outside the contact the surfaces are apart: no pressure (an element beyond b, since the edge element carries part of the last closed node's pressure); syy_depth: σ_z = −p₀ / √(1 + z²/b²) on the axis of a half-plane (Johnson 1985, eq. 4.49); the foundation is ten half-widths wide and deep, not a half-plane, and the stress is the nodal average of the elements around the node
|
||||
- **[nl-hybrid-incompressible](../tests/oracle/nl-hybrid-incompressible/)** (theory): Nearly incompressible hybrid block under prescribed stretch. Source: Uniaxial stress of the decoupled compressible neo-Hookean energy W = μ/2 (Ī₁ − 3) + κ/2 (J − 1)² (P. J. Flory, Trans. Faraday Soc. 57:829–838, 1961): σ = μ J^(−5/3) (λ² − I₁/3) + κ (J − 1) with the lateral stretch found so σ_yy = 0 (bisection; E = 3, ν = 0.4999: μ = 1.0000667, κ = 5000). Tolerances — sigma: a homogeneous deformation every hybrid hex8 represents exactly; the 27-element mesh makes the global mixed tangent indefinite in the first iterations (LDLᵀ): the tolerance admits the Newton tolerance and rounding; lateral: a homogeneous deformation every hybrid hex8 represents exactly; the 27-element mesh makes the global mixed tangent indefinite in the first iterations (LDLᵀ): the tolerance admits the Newton tolerance and rounding
|
||||
- **[nl-j2-uniaxial](../tests/oracle/nl-j2-uniaxial/)** (theory): Uniaxial tension of a J2 bilinear-hardening cube to large strain (implicit, finite strain). Source: J2 plasticity with linear isotropic hardening in uniaxial stress (Simo and Hughes, Computational Inelasticity, Springer 1998, §2.3) in the logarithmic strain, which Simo's exponential return map (CMAME 99:61–112, 1992) integrates exactly on a proportional path: Kirchhoff stress τ = σ_y + E_t (ε − σ_y/E), Cauchy stress σ = τ/J with ln J = τ/(3K) (Hencky's volume law). Tolerances — sigma: a homogeneous deformation the element represents exactly, reached on a proportional path: the tolerance only admits the Newton tolerance and rounding; plastic_strain: ε_p = (τ − σ_y)/H, as for the stress
|
||||
- **[nl-mooney-rivlin-modes](../tests/oracle/nl-mooney-rivlin-modes/)** (theory): Mooney–Rivlin block in uniaxial, equibiaxial and pure-shear tension. Source: Treloar's homogeneous modes of rubber testing (L. R. G. Treloar, The Physics of Rubber Elasticity, 3rd ed., Oxford 1975, ch. 10) for the decoupled compressible energy W = C₁₀ (Ī₁ − 3) + C₀₁ (Ī₂ − 3) + κ/2 (J − 1)²: principal Cauchy stresses σᵢ = (λᵢ/J) ∂W/∂λᵢ with the free stretch found so the free faces carry no stress (bisection; E = 3, ν = 0.49, C₀₁ = 0.2, C₁₀ = μ/2 − C₀₁). Tolerances — uniaxial: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding; uniaxial_lateral: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding; equibiaxial: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding; shear_xx: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding; shear_yy: a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding
|
||||
|
||||
+2
-2
@@ -55,7 +55,7 @@ products are run, no documentation text is copied). Status: **done**, **started*
|
||||
| Model | Steps: linear static, frequency; output presets | M3 | | done |
|
||||
| Model | Steps: nonlinear static, explicit dynamics, heat transfer; amplitudes | M7–M8, M15 | | started (nonlinear static with or without nonlinear geometry, increments, tolerances and a load path (cyclic loading), written to Abaqus `*STEP, NLGEOM` and LS-DYNA implicit (the load path as LS-DYNA's curve; refused by Abaqus for now), refused by Nastran; explicit dynamics; heat transfer; amplitudes per load planned) |
|
||||
| Interaction | Tie between non-matching meshes | M7 | | planned |
|
||||
| Interaction | Contact (general and pairs), friction, automatic pair detection | M7, M10 | | started (explicit: pairs, general and self contact, segment to segment with a penalty that keeps the time increment, Coulomb friction with exponential decay, friction on rigid walls, `interaction.contact.find`, Abaqus and LS-DYNA contact keywords; implicit contact in M7) |
|
||||
| Interaction | Contact (general and pairs), friction, automatic pair detection | M7, M10 | | started (explicit: pairs, general and self contact, segment to segment with a penalty that keeps the time increment, Coulomb friction with exponential decay, friction on rigid walls, `interaction.contact.find`, Abaqus and LS-DYNA contact keywords; implicit: frictionless mortar contact pairs in nonlinear static steps by an augmented Lagrangian, friction and self contact next) |
|
||||
| Interaction | Springs and dashpots (ground or two-point; DOF, vector or line), point masses with rotary inertia | M4 | | done (implicit; explicit translational; all three decks with what each cannot take reported) |
|
||||
| Interaction | Bolt pretension, connectors | M7 | | planned |
|
||||
| Decks | Abaqus input writer (`deck.write`, flat deck; reports what Abaqus cannot express) | M3 | | done |
|
||||
@@ -63,7 +63,7 @@ products are run, no documentation text is copied). Status: **done**, **started*
|
||||
| Decks | LS-DYNA keyword writer (implicit; explicit in M8) | M3 | | done (implicit static and eigenvalue; beam sections planned) |
|
||||
| Decks | Readers keeping unknown keywords | M9 | | planned |
|
||||
| Solve | Own linear static and modal solver, verified against analytic solutions | M4 | yes | started (solid elements: tet4, tet10, wedge6, hex8, hex20; 2D plane stress, plane strain and axisymmetric tri3, tri6, quad4 (full, incompatible modes), quad8 (full, reduced); quad4/tri3 MITC shells and Timoshenko beams with profiles, mixed with solids; reference points, kinematic and distributing couplings, moments; centrifugal loads) |
|
||||
| Solve | Own nonlinear implicit solver: Newton–Raphson with line search and automatic increments, total Lagrangian solids and 2D elements, mixed u–p at finite strain, follower pressure | M15 | yes | started (solids, plane strain, axisymmetric; St Venant–Kirchhoff, neo-Hookean and J2 plasticity (Simo's exponential return map at finite strain, radial return at small strain, consistent tangents, the return shared with explicit dynamics); verified by the elastica, tube inflation, patch and objectivity tests, uniaxial tension to large strain, Hill's thick cylinder, a cantilever's collapse and the Bauschinger effect; Mooney–Rivlin and Yeoh; thermal strain at finite and small strain; a symmetric indefinite LDLᵀ factorization with inertia, Newton through indefinite tangents (hybrid elements at ν = 0.4999 under prescribed displacement); linear buckling of solids (Euler columns, Bryan's plate) and imperfections from its modes; arc-length with critical points from the inertia (shallow-arch snap-through); shells, implicit contact next) |
|
||||
| Solve | Own nonlinear implicit solver: Newton–Raphson with line search and automatic increments, total Lagrangian solids and 2D elements, mixed u–p at finite strain, follower pressure | M15 | yes | started (solids, plane strain, axisymmetric; St Venant–Kirchhoff, neo-Hookean and J2 plasticity (Simo's exponential return map at finite strain, radial return at small strain, consistent tangents, the return shared with explicit dynamics); verified by the elastica, tube inflation, patch and objectivity tests, uniaxial tension to large strain, Hill's thick cylinder, a cantilever's collapse and the Bauschinger effect; frictionless mortar contact (patch test, Hertz); Mooney–Rivlin and Yeoh; thermal strain at finite and small strain; a symmetric indefinite LDLᵀ factorization with inertia, Newton through indefinite tangents (hybrid elements at ν = 0.4999 under prescribed displacement); linear buckling of solids (Euler columns, Bryan's plate) and imperfections from its modes; arc-length with critical points from the inertia (shallow-arch snap-through); shells and implicit friction next) |
|
||||
| Solve | Own explicit dynamics solver (central differences, one-point hex8 with hourglass control, nodal-pressure tet4, bulk viscosity, energy balance), verified against analytic wave and impact solutions | M10 | yes | started (X1 core and X2: large deformation, objective rates, J2 and Johnson–Cook plasticity, damage, erosion; X3: deformable contact and friction, verified by bar collision, sliding blocks, the contact patch test and Hertz; hyperelastic materials on the shared material point; opt-in mass scaling) |
|
||||
| Results | Deformed shape, contours, mode shapes, probes, reaction sums | M4 | | started (results in the session, `solve.probe`, reaction sums; display planned) |
|
||||
| Results | XY and path plots, cuts, display groups, free-body forces, animation | M9 | | planned |
|
||||
|
||||
@@ -1299,3 +1299,34 @@ from (cited again in the module docs); docs/fem.md describes the formulation.
|
||||
impact of spheres, H. Hertz, J. reine angew. Math. 92:156–171, 1882, and K. L. Johnson,
|
||||
*Contact Mechanics*, Cambridge 1985, §11.4; the sliding block, any dynamics text (J. L. Meriam,
|
||||
L. G. Kraige, *Engineering Mechanics: Dynamics*, §3/5).
|
||||
|
||||
## Part R: Contact in nonlinear static steps (M7), as implemented
|
||||
|
||||
The papers `fieldcraft_fem::mortar`, `fieldcraft_fem::dual` and `fieldcraft_solver::contact` are
|
||||
written from (cited again in the module docs); docs/fem.md describes the formulation.
|
||||
|
||||
- Mortar contact, segment to segment, with nodal weighted gaps and the pressure interpolated by
|
||||
the non-mortar side's shape functions: M. A. Puso, T. A. Laursen, *A mortar segment-to-segment
|
||||
contact method for large deformation solid mechanics*, CMAME 193:601–629, 2004; T. W. McDevitt,
|
||||
T. A. Laursen, *A mortar-finite element formulation for frictional contact problems*, IJNME
|
||||
48:1525–1547, 2000; the segmentation (projection on the non-mortar plane, clipping, integration
|
||||
cells) and the linearisation it needs, A. Popp, M. W. Gee, W. A. Wall, *A finite deformation
|
||||
mortar contact formulation using a primal–dual active set strategy*, IJNME 79:1354–1391, 2009.
|
||||
Chosen over two-pass node-to-surface because mortar passes the contact patch test on
|
||||
non-matching meshes (R. L. Taylor, P. Papadopoulos 1991; M. A. Crisfield 2000, as in Part Q).
|
||||
- The consistent tangent by automatic differentiation of the mortar integrals rather than by
|
||||
hand: J. Lengiewicz, J. Korelc, S. Stupkiewicz, *Automation of finite element formulations for
|
||||
large deformation contact problems*, IJNME 85:1252–1279, 2011; forward-mode (truncated Taylor)
|
||||
arithmetic, A. Griewank, A. Walther, *Evaluating Derivatives*, 2nd ed., SIAM 2008.
|
||||
- Augmented Lagrangian with Uzawa updates after each converged increment: J. C. Simo, T. A.
|
||||
Laursen, *An augmented Lagrangian treatment of contact problems involving friction*, Comput.
|
||||
Struct. 42(1):97–116, 1992; P. Wriggers, *Computational Contact Mechanics*, 2nd ed., Springer
|
||||
2006, ch. 6 and 10; T. A. Laursen, *Computational Contact and Impact Mechanics*, Springer 2003.
|
||||
- The active set inside Newton (the max() of the regularised pressure, a semismooth Newton
|
||||
method): P. Alart, A. Curnier, *A mixed formulation for frictional contact problems prone to
|
||||
Newton like solution methods*, CMAME 92:353–375, 1991; Popp et al. 2009.
|
||||
- Integration of the overlap cells: J. Radon's seven-point degree-5 rule on triangles (A. H.
|
||||
Stroud, *Approximate Calculation of Multiple Integrals*, Prentice-Hall 1971, T2:5-1).
|
||||
- Verification: Hertz's contact of cylinders and spheres, H. Hertz, J. reine angew. Math.
|
||||
92:156–171, 1882; K. L. Johnson, *Contact Mechanics*, Cambridge 1985, §4.2–4.3 (eqs. 4.45–4.49
|
||||
for the line contact's pressure and subsurface stresses).
|
||||
@@ -0,0 +1,10 @@
|
||||
# Contact patch test (implicit mortar contact, non-matching meshes)
|
||||
|
||||
Two unit cubes stacked along z, meshed independently: 3 × 3 × 2 hex8 below (graded in x and y),
|
||||
2 × 2 × 2 above, so the nodes of the interface at z = 1 do not match. A frictionless contact pair
|
||||
joins the lower block's top (main) and the upper block's bottom (secondary). The faces x = 0 and
|
||||
y = 0 of both blocks are symmetry planes, the base z = 0 is held in z, and the top z = 2 is pushed
|
||||
down by 0.02 (E = 1000, ν = 0.3) in two nonlinear static steps: `Small` without nonlinear
|
||||
geometry (small sliding, mortar integrals in the reference configuration) and `Finite` with it
|
||||
(finite sliding, searched and integrated on the deformed faces). The exact state is uniaxial
|
||||
stress, uniform in both blocks, with a uniform contact pressure equal to it.
|
||||
@@ -0,0 +1,432 @@
|
||||
{
|
||||
"title": "Contact patch test: two blocks with non-matching meshes in uniaxial compression (implicit mortar contact)",
|
||||
"kind": "theory",
|
||||
"source": "The contact patch test: a contact discretisation must transmit a uniform pressure across a non-matching interface exactly; Taylor & Papadopoulos, On a patch test for contact problems in two dimensions, Nonlinear Computational Mechanics, Springer 1991, 690–702; Crisfield, Re-visiting the contact patch test, IJNME 48:435–449, 2000; passed by mortar methods: Puso & Laursen, CMAME 193:601–629, 2004. Uniaxial stress between frictionless symmetry planes is uniform in both blocks",
|
||||
"quantities": [
|
||||
{
|
||||
"id": "small_lower_corner",
|
||||
"quantity": "Small: σ_zz of the lower block's corner element under the interface (element 10) over that of the upper block's corner element over it (element 19)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
10
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 1e-06
|
||||
},
|
||||
"reason": "small sliding is linear and its mortar integrals exact on these rectangular faces: a uniform stress is the discrete solution up to the convergence tolerance (10⁻¹⁰)"
|
||||
},
|
||||
{
|
||||
"id": "small_lower_centre",
|
||||
"quantity": "Small: σ_zz of the lower block's centre element under the interface (element 14) over that of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
14
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 1e-06
|
||||
},
|
||||
"reason": "as for the corner element"
|
||||
},
|
||||
{
|
||||
"id": "small_lower_base",
|
||||
"quantity": "Small: σ_zz of the lower block's bottom corner element (element 1) over that of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
1
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 1e-06
|
||||
},
|
||||
"reason": "as for the corner element"
|
||||
},
|
||||
{
|
||||
"id": "small_upper_top",
|
||||
"quantity": "Small: σ_zz of the upper block's top far corner element (element 26) over that of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
26
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 1e-06
|
||||
},
|
||||
"reason": "as for the corner element"
|
||||
},
|
||||
{
|
||||
"id": "small_lateral",
|
||||
"quantity": "Small: σ_xx of element 14 over its σ_zz (uniaxial stress: 0)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
14
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/0",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
14
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 0.0,
|
||||
"tolerance": {
|
||||
"absolute": 1e-06
|
||||
},
|
||||
"reason": "frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them"
|
||||
},
|
||||
{
|
||||
"id": "small_pressure",
|
||||
"quantity": "Small: the contact pressure at the secondary node (0.5, 0.5, 1) over −σ_zz of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"at": [
|
||||
[
|
||||
0.5,
|
||||
0.5,
|
||||
1.0
|
||||
]
|
||||
]
|
||||
},
|
||||
"pointer": "/nodes/0/contact/0/pressure",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"scale": -1.0
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 1e-06
|
||||
},
|
||||
"reason": "the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface"
|
||||
},
|
||||
{
|
||||
"id": "small_force",
|
||||
"quantity": "Small: the integrated contact pressure over the reaction at the pushed top",
|
||||
"measure": {
|
||||
"from": "small",
|
||||
"pointer": "/contacts/0/normal_force",
|
||||
"over": {
|
||||
"command": "results.reactions",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"sets": [
|
||||
"top"
|
||||
]
|
||||
},
|
||||
"pointer": "/sets/0/force/2",
|
||||
"scale": -1.0
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 1e-06
|
||||
},
|
||||
"reason": "the pressure carries the whole load across the interface"
|
||||
},
|
||||
{
|
||||
"id": "finite_lower_corner",
|
||||
"quantity": "Finite: σ_zz of the lower block's corner element under the interface (element 10) over that of the upper block's corner element over it (element 19)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
10
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0002
|
||||
},
|
||||
"reason": "finite sliding is exact up to the geometric terms of the gaps the augmentation leaves (10⁻⁵ of the element thickness) and the default convergence tolerances"
|
||||
},
|
||||
{
|
||||
"id": "finite_lower_centre",
|
||||
"quantity": "Finite: σ_zz of the lower block's centre element under the interface (element 14) over that of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
14
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0002
|
||||
},
|
||||
"reason": "as for the corner element"
|
||||
},
|
||||
{
|
||||
"id": "finite_lower_base",
|
||||
"quantity": "Finite: σ_zz of the lower block's bottom corner element (element 1) over that of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
1
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0002
|
||||
},
|
||||
"reason": "as for the corner element"
|
||||
},
|
||||
{
|
||||
"id": "finite_upper_top",
|
||||
"quantity": "Finite: σ_zz of the upper block's top far corner element (element 26) over that of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
26
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0002
|
||||
},
|
||||
"reason": "as for the corner element"
|
||||
},
|
||||
{
|
||||
"id": "finite_lateral",
|
||||
"quantity": "Finite: σ_xx of element 14 over its σ_zz (uniaxial stress: 0)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
14
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/0",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
14
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
}
|
||||
},
|
||||
"value": 0.0,
|
||||
"tolerance": {
|
||||
"absolute": 0.0002
|
||||
},
|
||||
"reason": "frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them"
|
||||
},
|
||||
{
|
||||
"id": "finite_pressure",
|
||||
"quantity": "Finite: the contact pressure at the secondary node (0.5, 0.5, 1) over −σ_zz of element 19",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"at": [
|
||||
[
|
||||
0.5,
|
||||
0.5,
|
||||
1.0
|
||||
]
|
||||
]
|
||||
},
|
||||
"pointer": "/nodes/0/contact/0/pressure",
|
||||
"over": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2",
|
||||
"scale": -1.0
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0002
|
||||
},
|
||||
"reason": "the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface"
|
||||
},
|
||||
{
|
||||
"id": "finite_force",
|
||||
"quantity": "Finite: the integrated contact pressure over the reaction at the pushed top",
|
||||
"measure": {
|
||||
"from": "finite",
|
||||
"pointer": "/contacts/0/normal_force",
|
||||
"over": {
|
||||
"command": "results.reactions",
|
||||
"params": {
|
||||
"step": "Finite",
|
||||
"sets": [
|
||||
"top"
|
||||
]
|
||||
},
|
||||
"pointer": "/sets/0/force/2",
|
||||
"scale": -1.0
|
||||
}
|
||||
},
|
||||
"value": 1.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0002
|
||||
},
|
||||
"reason": "the pressure carries the whole load across the interface"
|
||||
},
|
||||
{
|
||||
"id": "small_stress",
|
||||
"quantity": "Small: σ_zz of element 19 (uniaxial stress E ε = −10 for the 1% squeeze)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Small",
|
||||
"elements": [
|
||||
19
|
||||
]
|
||||
},
|
||||
"pointer": "/elements/0/stress/0/2"
|
||||
},
|
||||
"value": -10.0,
|
||||
"tolerance": {
|
||||
"relative": 0.0001
|
||||
},
|
||||
"reason": "the squeeze less the penetration the augmented Lagrangian leaves (up to 10⁻⁵ of the element thickness, a few 10⁻⁵ of the squeeze)"
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,65 @@
|
||||
{
|
||||
"note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
|
||||
"values": {
|
||||
"finite_force": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999999999974551
|
||||
},
|
||||
"finite_lateral": {
|
||||
"band": 0.0002,
|
||||
"value": 1.223600676667172e-6
|
||||
},
|
||||
"finite_lower_base": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999905821256437
|
||||
},
|
||||
"finite_lower_centre": {
|
||||
"band": 1e-9,
|
||||
"value": 0.999987114528879
|
||||
},
|
||||
"finite_lower_corner": {
|
||||
"band": 1.000001514518151e-9,
|
||||
"value": 1.000001514518151
|
||||
},
|
||||
"finite_pressure": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999828003418422
|
||||
},
|
||||
"finite_upper_top": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999912761681571
|
||||
},
|
||||
"small_force": {
|
||||
"band": 1.0000000000000607e-9,
|
||||
"value": 1.0000000000000606
|
||||
},
|
||||
"small_lateral": {
|
||||
"band": 1e-6,
|
||||
"value": 7.880554574306202e-15
|
||||
},
|
||||
"small_lower_base": {
|
||||
"band": 1e-9,
|
||||
"value": 0.999999999999944
|
||||
},
|
||||
"small_lower_centre": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999999999999398
|
||||
},
|
||||
"small_lower_corner": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999999999999855
|
||||
},
|
||||
"small_pressure": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999999999999953
|
||||
},
|
||||
"small_stress": {
|
||||
"band": 1e-8,
|
||||
"value": -9.99957382191768
|
||||
},
|
||||
"small_upper_top": {
|
||||
"band": 1e-9,
|
||||
"value": 0.9999999999999263
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,24 @@
|
||||
[
|
||||
{"command": "mesh.block", "params": {"body": "Lower", "kind": "hex8", "corners": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1]], "divisions": [3, 3, 2], "faces": {"1": "bottom", "2": "top", "3": "y0", "6": "x0"}, "bias": [2.0, 0.6, 1.0]}},
|
||||
{"command": "mesh.block", "params": {"body": "Upper", "kind": "hex8", "corners": [[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1], [0, 0, 2], [1, 0, 2], [1, 1, 2], [0, 1, 2]], "divisions": [2, 2, 2], "faces": {"1": "bottom", "2": "top", "3": "y0", "6": "x0"}, "merge": 0}},
|
||||
{"command": "model.set.create", "params": {"name": "lower", "geometry": [{"body": "Lower"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "upper", "geometry": [{"body": "Upper"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "lower_top", "geometry": [{"body": "Lower", "face": "top"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "upper_bottom", "geometry": [{"body": "Upper", "face": "bottom"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "x0", "geometry": [{"body": "Lower", "face": "x0"}, {"body": "Upper", "face": "x0"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "y0", "geometry": [{"body": "Lower", "face": "y0"}, {"body": "Upper", "face": "y0"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "z0", "geometry": [{"body": "Lower", "face": "bottom"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "top", "geometry": [{"body": "Upper", "face": "top"}]}},
|
||||
{"command": "model.material.create", "params": {"name": "Mat", "elastic": {"type": "isotropic", "young": 1000.0, "poisson": 0.3}}},
|
||||
{"command": "model.section.create", "params": {"name": "lower", "set": "lower", "material": "Mat", "kind": {"type": "solid"}}},
|
||||
{"command": "model.section.create", "params": {"name": "upper", "set": "upper", "material": "Mat", "kind": {"type": "solid"}}},
|
||||
{"command": "interaction.contact.pair", "params": {"name": "interface", "main": "lower_top", "secondary": "upper_bottom"}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "x0", "type": "displacement", "target": {"set": "x0"}, "values": [0, null, null, null, null, null]}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "y0", "type": "displacement", "target": {"set": "y0"}, "values": [null, 0, null, null, null, null]}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "z0", "type": "displacement", "target": {"set": "z0"}, "values": [null, null, 0, null, null, null]}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "push", "type": "displacement", "target": {"set": "top"}, "values": [null, null, -0.02, null, null, null]}},
|
||||
{"command": "model.step.create", "params": {"name": "Small", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": false, "tolerances": {"force": 1e-10, "displacement": 1e-08, "energy": 1e-16}}, "boundary_conditions": ["x0", "y0", "z0", "push"], "loads": []}},
|
||||
{"command": "model.step.create", "params": {"name": "Finite", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": true}, "boundary_conditions": ["x0", "y0", "z0", "push"], "loads": []}},
|
||||
{"command": "solve.nonlinear", "params": {"step": "Small"}, "id": "small"},
|
||||
{"command": "solve.nonlinear", "params": {"step": "Finite"}, "id": "finite"}
|
||||
]
|
||||
@@ -0,0 +1,11 @@
|
||||
# Hertz line contact: cylinder on a flat (implicit mortar contact)
|
||||
|
||||
A steel cylinder of radius R = 10 mm pressed on a steel block (E = 210 GPa, ν = 0.3; mm, N, MPa)
|
||||
in plane strain: a quarter model of the cylinder's lower part (a 2.5 mm wide block whose bottom
|
||||
is the circular arc, graded towards the contact) on a 5 × 5 mm foundation, symmetric about
|
||||
x = 0, one element thick with every node held in z. A pressure on the indenter's top carries
|
||||
the load P = 2265.57 N/mm (per length of the whole cylinder) chosen so that Hertz's half-width is
|
||||
b = 0.5 mm and the peak pressure p₀ = 2884.6 MPa. Soft springs (0.01 N/mm per node) hold the
|
||||
indenter's top vertically until the contact closes. One nonlinear static step without nonlinear
|
||||
geometry: small sliding, mortar contact of the round face (secondary) on the flat (main) by an
|
||||
augmented Lagrangian.
|
||||
@@ -0,0 +1,109 @@
|
||||
{
|
||||
"title": "Hertz line contact: a cylinder pressed on a flat (implicit mortar contact, plane strain)",
|
||||
"kind": "theory",
|
||||
"source": "H. Hertz, Über die Berührung fester elastischer Körper, J. reine angew. Math. 92:156–171, 1882; K. L. Johnson, Contact Mechanics, Cambridge University Press 1985, §4.3 (two-dimensional contact of cylindrical bodies, eqs. 4.45–4.49): b = √(4PR/(πE*)), p₀ = 2P/(πb), with 1/E* = 2(1 − ν²)/E for two bodies of one material and R the cylinder's radius on a flat",
|
||||
"quantities": [
|
||||
{
|
||||
"id": "peak_pressure",
|
||||
"quantity": "the largest contact pressure p₀ (at x = 0)",
|
||||
"measure": {
|
||||
"from": "solve",
|
||||
"pointer": "/contacts/0/max_pressure/value"
|
||||
},
|
||||
"value": 2884.6153846153843,
|
||||
"tolerance": {
|
||||
"relative": 0.02
|
||||
},
|
||||
"reason": "p₀ = 2P/(πb) for the load per length P = 2265.57 N/mm, b = 0.5 mm; the contact width spans seven elements of the graded mesh"
|
||||
},
|
||||
{
|
||||
"id": "normal_force",
|
||||
"quantity": "the force across the contact (half model, 1 mm thick)",
|
||||
"measure": {
|
||||
"from": "solve",
|
||||
"pointer": "/contacts/0/normal_force"
|
||||
},
|
||||
"value": 1132.7858125924733,
|
||||
"tolerance": {
|
||||
"relative": 0.002
|
||||
},
|
||||
"reason": "the pressure carries the whole load; the soft springs that hold the indenter before contact take a millionth"
|
||||
},
|
||||
{
|
||||
"id": "pressure_x0296",
|
||||
"quantity": "the contact pressure at the secondary node at x = 0.29594 (node 7)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Press",
|
||||
"nodes": [
|
||||
7
|
||||
]
|
||||
},
|
||||
"pointer": "/nodes/0/contact/0/pressure"
|
||||
},
|
||||
"value": 2325.066800691437,
|
||||
"tolerance": {
|
||||
"relative": 0.05
|
||||
},
|
||||
"reason": "p₀ √(1 − x²/b²) at the node; the nodal pressure (the node's normal force over the area it carries) averages the distribution over the node's elements"
|
||||
},
|
||||
{
|
||||
"id": "pressure_x0367",
|
||||
"quantity": "the contact pressure at the secondary node at x = 0.36701 (node 8)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Press",
|
||||
"nodes": [
|
||||
8
|
||||
]
|
||||
},
|
||||
"pointer": "/nodes/0/contact/0/pressure"
|
||||
},
|
||||
"value": 1959.0164149439815,
|
||||
"tolerance": {
|
||||
"relative": 0.1
|
||||
},
|
||||
"reason": "as at node 7, nearer the edge, where the elements round off the square-root fall of the pressure to zero at b"
|
||||
},
|
||||
{
|
||||
"id": "pressure_x0633",
|
||||
"quantity": "the contact pressure at the secondary node at x = 0.63325 (node 11, beyond the half-width b = 0.5)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Press",
|
||||
"nodes": [
|
||||
11
|
||||
]
|
||||
},
|
||||
"pointer": "/nodes/0/contact/0/pressure"
|
||||
},
|
||||
"value": 0.0,
|
||||
"tolerance": {
|
||||
"absolute": 1.0
|
||||
},
|
||||
"reason": "outside the contact the surfaces are apart: no pressure (an element beyond b, since the edge element carries part of the last closed node's pressure)"
|
||||
},
|
||||
{
|
||||
"id": "syy_depth",
|
||||
"quantity": "the vertical stress σ_yy under the centre of contact at depth 0.47127 (node 713)",
|
||||
"measure": {
|
||||
"command": "solve.probe",
|
||||
"params": {
|
||||
"step": "Press",
|
||||
"nodes": [
|
||||
713
|
||||
]
|
||||
},
|
||||
"pointer": "/nodes/0/stress/1"
|
||||
},
|
||||
"value": -2099.1580228637245,
|
||||
"tolerance": {
|
||||
"relative": 0.04
|
||||
},
|
||||
"reason": "σ_z = −p₀ / √(1 + z²/b²) on the axis of a half-plane (Johnson 1985, eq. 4.49); the foundation is ten half-widths wide and deep, not a half-plane, and the stress is the nodal average of the elements around the node"
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,29 @@
|
||||
{
|
||||
"note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
|
||||
"values": {
|
||||
"normal_force": {
|
||||
"band": 1.133036636011328e-6,
|
||||
"value": 1133.0366360113278
|
||||
},
|
||||
"peak_pressure": {
|
||||
"band": 2.891953889449524e-6,
|
||||
"value": 2891.953889449524
|
||||
},
|
||||
"pressure_x0296": {
|
||||
"band": 2.325066800691437e-6,
|
||||
"value": 2257.8357909118563
|
||||
},
|
||||
"pressure_x0367": {
|
||||
"band": 2.0784005834495077e-6,
|
||||
"value": 2078.4005834495074
|
||||
},
|
||||
"pressure_x0633": {
|
||||
"band": 1.0,
|
||||
"value": -0.0
|
||||
},
|
||||
"syy_depth": {
|
||||
"band": 2.0991580228637247e-6,
|
||||
"value": -2059.819639241533
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,23 @@
|
||||
[
|
||||
{"command": "mesh.block", "params": {"body": "Indenter", "kind": "hex8", "corners": [[0, 0, 0], [2.5, 0.3175416344814579, 0], [2.5, 3.0, 0], [0, 3.0, 0], [0, 0, 1.0], [2.5, 0.3175416344814579, 1.0], [2.5, 3.0, 1.0], [0, 3.0, 1.0]], "divisions": [20, 10, 1], "bias": [8, 8, 1], "edges": [{"corners": [1, 2], "arc": {"center": [0, 10.0, 0]}}, {"corners": [5, 6], "arc": {"center": [0, 10.0, 1.0]}}], "faces": {"3": "round", "5": "top", "6": "sym"}}},
|
||||
{"command": "mesh.block", "params": {"body": "Foundation", "kind": "hex8", "corners": [[0, -5, 0], [5, -5, 0], [5, 0, 0], [0, 0, 0], [0, -5, 1.0], [5, -5, 1.0], [5, 0, 1.0], [0, 0, 1.0]], "divisions": [24, 14, 1], "bias": [10, 0.1, 1], "faces": {"3": "base", "5": "flat", "6": "sym"}, "merge": 0}},
|
||||
{"command": "model.set.create", "params": {"name": "indenter", "geometry": [{"body": "Indenter"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "foundation", "geometry": [{"body": "Foundation"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "all", "geometry": [{"body": "Indenter"}, {"body": "Foundation"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "round", "geometry": [{"body": "Indenter", "face": "round"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "flat", "geometry": [{"body": "Foundation", "face": "flat"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "top", "geometry": [{"body": "Indenter", "face": "top"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "base", "geometry": [{"body": "Foundation", "face": "base"}]}},
|
||||
{"command": "model.set.create", "params": {"name": "sym", "geometry": [{"body": "Indenter", "face": "sym"}, {"body": "Foundation", "face": "sym"}]}},
|
||||
{"command": "model.material.create", "params": {"name": "Steel", "elastic": {"type": "isotropic", "young": 210000.0, "poisson": 0.3}}},
|
||||
{"command": "model.section.create", "params": {"name": "indenter", "set": "indenter", "material": "Steel", "kind": {"type": "solid"}}},
|
||||
{"command": "model.section.create", "params": {"name": "foundation", "set": "foundation", "material": "Steel", "kind": {"type": "solid"}}},
|
||||
{"command": "interaction.contact.pair", "params": {"name": "hertz", "main": "flat", "secondary": "round"}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "sym", "type": "displacement", "target": {"set": "sym"}, "values": [0, null, null, null, null, null]}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "plane", "type": "displacement", "target": {"set": "all"}, "values": [null, null, 0, null, null, null]}},
|
||||
{"command": "model.boundary_condition.create", "params": {"name": "base", "type": "displacement", "target": {"set": "base"}, "values": [null, 0, null, null, null, null]}},
|
||||
{"command": "model.spring.create", "params": {"name": "hold", "type": "spring", "first": {"set": "top"}, "direction": {"dof": 2}, "stiffness": 0.01}},
|
||||
{"command": "model.load.create", "params": {"name": "press", "type": "pressure", "set": "top", "magnitude": 453.1143250369893}},
|
||||
{"command": "model.step.create", "params": {"name": "Press", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": false, "max_iterations": 60}, "boundary_conditions": ["sym", "plane", "base"], "loads": ["press"]}},
|
||||
{"command": "solve.nonlinear", "params": {"step": "Press"}, "id": "solve"}
|
||||
]
|
||||
Reference in new issue
Block a user