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 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
8 lines
507 B
Markdown
8 lines
507 B
Markdown
# Nonlinear patch test, hex8
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A unit cube of 3 × 3 × 3 hex8 elements whose non-corner nodes are moved off the lattice, so no
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element is a parallelepiped. Every boundary node is prescribed u = (F − I) X with
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F = [[1.3, 0.2, -0.1], [-0.15, 0.9, 0.25], [0.05, -0.2, 1.1]] (stretch, shear and rotation, J = 1.389000); the eight inner nodes are free. The neo-Hookean
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material (E = 100, ν = 0.3) must take the homogeneous deformation: the inner node 22 moves by
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(F − I) X and the Cauchy stress is uniform.
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