forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
ce8e23d05b
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 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
18 lines
1.5 KiB
JSON
18 lines
1.5 KiB
JSON
{
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"title": "Neo-Hookean cube stretched to λ = 1.5: explicit dynamics, loaded slowly, against the implicit nonlinear solver",
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"kind": "theory",
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"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",
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"quantities": [
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{"id": "lateral", "quantity": "lateral displacement of the corner (1, 1, 1) along y, explicit over implicit",
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"measure": {"command": "solve.probe", "params": {"step": "Dynamic", "at": [[1, 1, 1]]}, "pointer": "/nodes/0/displacement/1",
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"over": {"command": "solve.probe", "params": {"step": "Static", "at": [[1, 1, 1]]}, "pointer": "/nodes/0/displacement/1"}},
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"value": 1.0, "tolerance": {"relative": 0.005},
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"reason": "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"},
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{"id": "stress", "quantity": "σ_xx of element 1, explicit, over σ_xx at the node at (0, 0, 0), implicit",
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"measure": {"command": "solve.probe", "params": {"step": "Dynamic", "elements": [1]}, "pointer": "/elements/0/stress/0",
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"over": {"command": "solve.probe", "params": {"step": "Static", "at": [[0, 0, 0]]}, "pointer": "/nodes/0/stress/0"}},
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"value": 1.0, "tolerance": {"relative": 0.005},
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"reason": "as for the displacement"}
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]
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}
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