forked from 1b-agent/fieldcraft-upstream
verification: nonlinear oracle cases and the nonlinear solver's documentation
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
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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{
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"title": "Nonlinear patch test, hex8: a homogeneous finite deformation of a distorted mesh",
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"kind": "theory",
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"source": "The patch test (B. M. Irons, A. Razzaque, in A. K. Aziz (ed.), The Mathematical Foundations of the Finite Element Method, Academic Press 1972, 557–587) at finite strain: a boundary moved by x = F X makes F the solution everywhere (J. Bonet, R. D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd ed., Cambridge 2008, §8); the neo-Hookean Cauchy stress σ = μ J^(−5/3) dev b + κ (J − 1) I of that F",
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"command": "solve.probe",
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"params": {
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"step": "Deform",
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22
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"pointer": "/nodes/0/displacement/0"
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"value": 0.13583340405268285,
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"tolerance": {
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"relative": 1e-08
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},
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"reason": "a patch test is passed exactly: the tolerance admits rounding and the Newton tolerance"
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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",
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"measure": {
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"command": "solve.probe",
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"params": {
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{
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"id": "uz",
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"quantity": "u_z at inner node 22",
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"measure": {
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"command": "solve.probe",
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"reason": "a patch test is passed exactly: the tolerance admits rounding and the Newton tolerance"
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},
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{
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"id": "sxx",
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"quantity": "Cauchy σ_xx 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": "Deform",
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"pointer": "/nodes/0/stress/0"
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"reason": "a patch test is passed exactly: the tolerance admits rounding and the Newton tolerance"
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},
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{
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"id": "syy",
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"quantity": "Cauchy σ_yy 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": "Deform",
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},
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{
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"id": "szz",
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"quantity": "Cauchy σ_zz 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": "Deform",
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"pointer": "/nodes/0/stress/2"
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},
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{
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"id": "sxy",
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"quantity": "Cauchy σ_xy 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": "Deform",
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"pointer": "/nodes/0/stress/3"
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"reason": "a patch test is passed exactly: the tolerance admits rounding and the Newton tolerance"
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},
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{
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"id": "sxz",
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"quantity": "Cauchy σ_xz 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": "Deform",
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"nodes": [
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22
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"pointer": "/nodes/0/stress/4"
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"tolerance": {
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"reason": "a patch test is passed exactly: the tolerance admits rounding and the Newton tolerance"
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},
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{
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"id": "syz",
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"quantity": "Cauchy σ_yz 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": "Deform",
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"nodes": [
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22
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"pointer": "/nodes/0/stress/5"
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"tolerance": {
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"relative": 1e-07
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},
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"reason": "a patch test is passed exactly: the tolerance admits rounding and the Newton tolerance"
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}
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]
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}
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