explicit: hyperelastic materials on the shared finite-strain material point

Neo-Hookean, Mooney–Rivlin and Yeoh materials in explicit dynamics, in
total form from the deformation gradient (objective by construction):
the one-point hex8 takes its mean F over the undeformed element and the
stress τ/J; tet4 takes the isochoric stress of its own F with the
average nodal pressure of the decoupled volumetric energy (Bonet–Burton
at finite strain). Each element's frequency bound follows the tangent's
largest normal stiffness. Small-displacement steps and thermal strain of
hyperelastic elements are refused by name.

Verified by uniaxial strain to λ = 1.5 of all three laws on hex8 and
tet4 against the material point (to rounding), and the oracle case
explicit-neo-hookean-implicit: a quasi-static explicit pull against the
implicit nonlinear solver (lateral contraction to 0.09%, stress to 0.03%).

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

docs/oracle.md

@@ -2,7 +2,7 @@
 
 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.
 
-**199 of 205 quantities pass** (6 known failure(s)) in 61 active cases: 52 theory, 9 published benchmark, 0 experiment; 10 pending cases wait for capabilities still being built.
+**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.
 
 ## Theory: closed-form solutions, patch tests and mesh invariants
 
@@ -46,6 +46,8 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
 | [explicit-contact-patch](../tests/oracle/explicit-contact-patch/) | σ_zz of the upper block's top far corner element (element 26) over that of element 19 | 1 | 0.99944 | -0.0564% | 0.5% | pass | matches |
 | [explicit-contact-patch](../tests/oracle/explicit-contact-patch/) | the force across the interface over −σ_zz A (A = 1) | 1 | 1.0026 | 0.259% | 1% | pass | matches |
 | [explicit-contact-patch](../tests/oracle/explicit-contact-patch/) | σ_xx of element 14 over its σ_zz (uniaxial stress: 0) | 0 | -3.6052e-4 | -3.6e-4 | ± 0.005 | pass | matches |
+| [explicit-neo-hookean-implicit](../tests/oracle/explicit-neo-hookean-implicit/) | lateral displacement of the corner (1, 1, 1) along y, explicit over implicit | 1 | 0.99908 | -0.0922% | 0.5% | pass | matches |
+| [explicit-neo-hookean-implicit](../tests/oracle/explicit-neo-hookean-implicit/) | σ_xx of element 1, explicit, over σ_xx at the node at (0, 0, 0), implicit | 1 | 1.0003 | 0.0255% | 0.5% | pass | matches |
 | [explicit-sliding-block-contact](../tests/oracle/explicit-sliding-block-contact/) | distance travelled (top centre node) against ∫ v dv / (g μ(v)) = 2.01524 | 2.0152 | 2.0118 | -0.172% | 1% | pass | matches |
 | [explicit-sliding-block-contact](../tests/oracle/explicit-sliding-block-contact/) | velocity of the top centre node after the stop | 0 | ≈ 0 | ≈ 0 | ± 0.03 | pass | matches |
 | [explicit-sliding-block-wall](../tests/oracle/explicit-sliding-block-wall/) | distance travelled (top centre node) against v₀²/(2μg) = 1.5 | 1.5 | 1.4999 | -0.0053% | 1% | pass | matches |
@@ -235,6 +237,7 @@ Generated by `cargo xtask oracle` from [`tests/oracle/`](../tests/oracle/); the
 - **[cdt-stepped-block](../tests/oracle/cdt-stepped-block/)** (theory): Constrained Delaunay mesh of a stepped block: exact volume, valid elements. Source: mesh invariants: a tetrahedralization of a polyhedron fills its volume exactly (Si, TetGen paper ACM TOMS 41(2) 2015 for the definition of a CDT; Diazzi et al., ACM TOG 42(6) 2023); the volume is 60·40·10 + 40·40·10 + 20·40·10 − 10·10·10. Tolerances — volume: a planar boundary is tessellated exactly and the constrained Delaunay mesh fills it exactly: only rounding; invalid: every element of a valid mesh has positive volume; undetermined: a linear tetrahedron's sign is exact
 - **[explicit-bars-collision](../tests/oracle/explicit-bars-collision/)** (theory): Two identical elastic bars colliding (explicit contact). Source: One-dimensional elastic impact of equal bars: contact for 2L/c, interface force ρcAv₀/2, exchange of velocities, no loss of energy; Graff, Wave Motion in Elastic Solids, Dover 1991, §2.1–2.3; Johnson, Impact Strength of Materials, Arnold 1972, §1.6. Tolerances — duration: the penalty springs at the interface delay the release by a few element transit times (about 1% of 2L/c with 200 elements per bar); force: the plateau is ρcAv₀/2 to 0.01%; the peak is the plateau plus the ringing behind the discrete wave front, a few percent; v_a: the striker stops on average (its kinetic energy is under 0.01% of the start's, see ke); its far end node keeps the ringing of the discrete release front, a few percent of v₀; v_b: the struck bar leaves at v₀ on average; its far end node keeps the ringing of the discrete wave fronts, a few percent; ke: an elastic impact keeps the kinetic energy; the quadratic bulk viscosity at the compression fronts and the vibration left in the bars take a fraction of a percent; contact_energy: the penalty springs give back what they took; the trapezoidal work of a spring that engages between increments drifts by far less than 0.1%
 - **[explicit-contact-patch](../tests/oracle/explicit-contact-patch/)** (theory): Contact patch test: two blocks with non-matching meshes in uniaxial compression (explicit 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. Uniaxial stress between frictionless symmetry planes is uniform in both blocks. Tolerances — lower_corner: a uniform stress is an equilibrium of the discrete system (the integrated contact forces are the consistent nodal forces of a uniform pressure on both meshes); what is left is the ringing of the loading, a hundred wave transits slow; lower_centre: as for the corner element; lower_base: as for the corner element; upper_top: as for the corner element; force: the integrated contact pressure carries the whole load; the largest force of the run is the final one in a slow squeeze, up to the ringing; lateral: frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them
+- **[explicit-neo-hookean-implicit](../tests/oracle/explicit-neo-hookean-implicit/)** (theory): Neo-Hookean cube stretched to λ = 1.5: explicit dynamics, loaded slowly, against the implicit nonlinear solver. Source: Uniaxial stress of a compressible neo-Hookean solid (Holzapfel, Nonlinear Solid Mechanics, Wiley 2000, §6.5): a homogeneous state that a quasi-static explicit run must share with the implicit Newton solution on the same material point; the implicit solver is itself checked against the closed form by nl-neo-hookean-uniaxial. Tolerances — lateral: the same material point and a homogeneous state; the explicit run is pulled over a few hundred wave transits, and what is left of its waves is a fraction of a percent; stress: as for the displacement
 - **[explicit-sliding-block-contact](../tests/oracle/explicit-sliding-block-contact/)** (theory): Block sliding to a stop on a deformable plate, friction decaying with the slip rate (explicit contact). Source: A rigid block launched at v₀ with friction μ(v) = μk + (μs − μk) e^(−d v) decelerates at g μ(v); it travels ∫₀^v₀ v dv / (g μ(v)) (Simpson's rule, 200 000 intervals) and stops after [v₀ + ln((μk + (μs − μk) e^(−d v₀))/μs)/d]/(g μk) = 1.2001; Meriam & Kraige, Engineering Mechanics: Dynamics, §3/5; the exponential decay law as in Oden & Martins, CMAME 52:527–634, 1985. Tolerances — distance: the block bounces on the penalty springs and the plate under it shears elastically, so the normal force and the slip rate it feels vary by a little around their rigid-body values; velocity: the block sticks; what is left is its elastic vibration, under 1% of v₀
 - **[explicit-sliding-block-wall](../tests/oracle/explicit-sliding-block-wall/)** (theory): Block sliding to a stop on a rigid wall with Coulomb friction (explicit). Source: A rigid block launched at v₀ on a horizontal plane with Coulomb friction μ decelerates at μg and stops after v₀/(μg) at v₀²/(2μg), its kinetic energy all dissipated by friction; Meriam & Kraige, Engineering Mechanics: Dynamics, §3/5 (work and energy). Tolerances — distance: the wall's friction impulses are exact Coulomb impulses; the block's elastic vibration from the sudden gravity and the friction moment move the node by a fraction of a percent; velocity: the block sticks; what is left is its elastic vibration, under 1% of v₀; dissipated: the kinetic energy goes into friction; the vibration and the work of gravity as the block settles add or take a fraction of a percent
 - **[filleted-bracket-fillet-stress](../tests/oracle/filleted-bracket-fillet-stress/)** (theory): Filleted L-bracket under a side load: the peak von Mises stress on the R6 fillet, fine tet10 mesh. Source: mesh convergence of the finite element solution (P. J. Roache, Verification and Validation in Computational Science and Engineering, Hermosa, 1998, ch. 5): the bracket has no closed-form stress; the reference is the mesh-independent peak of a four-level study of quadratic tetrahedral meshes refined by √2 in size and in curvature resolution (README.md); equilibrium. Tolerances — fillet_peak: the four-level study gives 213.3, 210.6, 214.3, 213.3 MPa (2k to 13.5k elements): the bending stress is converged across the fillet, and the peak nodal value moves only with which of the fillet's tessellation lines (fixed angles, through every level) carries the largest node, by under 2%; reaction: equilibrium holds to rounding