forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
8ca2dddeec
Theory cases for the nonlinear solver, each frozen as a fixture: uniaxial stretch of a neo-Hookean block to twice its length (closed form), the nonlinear patch test on a distorted hex8 mesh, a quarter turn of the same mesh (objectivity: zero stress), the elastica of a hex20 cantilever at P L²/(E I) = 1, 2, 5, 10 against Bisshopp–Drucker (0.2–0.5 %), and the inflation of a thick neo-Hookean tube by a follower pressure against Rivlin's closed form (0.08 % at the bore). A finite-strain Cook's membrane is pending its transcribed reference. docs/fem.md describes the formulation, the material point interface, the follower-pressure choice and what nonlinear steps refuse; the literature, parity and roadmap pages follow. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
84 lines
2.0 KiB
JSON
84 lines
2.0 KiB
JSON
{
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"title": "A quarter turn strains and stresses nothing (objectivity)",
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"kind": "theory",
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"source": "Objectivity of the total Lagrangian formulation and of the hyperelastic stress: a rigid motion x = R X + c gives C = I and σ = 0 whatever the rotation (Bonet & Wood 2008, §3.4 and §5.2; T. Belytschko, W. K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, 2nd ed., Wiley 2014, §5.5)",
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"quantities": [
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{
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"id": "ux",
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"quantity": "u_x at inner node 22: the rotation's",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Turn",
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"nodes": [
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22
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]
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},
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"pointer": "/nodes/0/displacement/0"
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},
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"value": -0.011149180525904245,
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"tolerance": {
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"absolute": 1e-09
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},
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"reason": "the inner nodes follow the rigid rotation exactly"
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},
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{
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"id": "uy",
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"quantity": "u_y at inner node 22: the rotation's",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Turn",
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"nodes": [
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22
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]
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},
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"pointer": "/nodes/0/displacement/1"
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},
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"value": 0.07859051161172886,
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"tolerance": {
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"absolute": 1e-09
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},
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"reason": "the inner nodes follow the rigid rotation exactly"
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},
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{
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"id": "uz",
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"quantity": "u_z at inner node 22: the rotation's",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Turn",
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"nodes": [
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22
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]
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},
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"pointer": "/nodes/0/displacement/2"
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},
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"value": -0.06744133108582467,
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"tolerance": {
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"absolute": 1e-09
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},
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"reason": "the inner nodes follow the rigid rotation exactly"
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},
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{
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"id": "von_mises",
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"quantity": "von Mises stress at inner node 22",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Turn",
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"nodes": [
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22
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]
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},
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"pointer": "/nodes/0/von_mises"
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},
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"value": 0.0,
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"tolerance": {
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"absolute": 1e-08
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},
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"reason": "zero up to rounding of stresses of order E = 1000: a 90° turn leaves no strain"
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}
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]
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}
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