Solid Mechanics¶
Four worked solid-mechanics examples in examples/solid/, built
as a progressive ladder — each rung adds exactly one new concept on
top of the previous one:
Cantilever Beam — linear elasticity, one direct solve. The baseline.
Hyperelastic Beam — finite strain (Neo-Hookean); introduces the L-BFGS energy-minimization recipe.
Hertzian Contact — adds a constraint (contact penalty) and a closed-form verification, reusing the same L-BFGS recipe.
Plasticity (J2) — adds path-dependence: per-quadrature history variables and a variational constitutive update, in 2D and 3D.
Together they cover the two solver patterns TensorMesh uses for solid problems:
Direct linear solve for small-strain linear elasticity (
cantilever_beam).L-BFGS energy minimization for nonlinear problems where the potential energy is well-defined — hyperelasticity, contact, and plasticity (
hyperelastic_beam,hertzian_contact,plasticity_strip).
The order below mirrors solver complexity.
Linear elasticity, steel cantilever with a tip load — the simplest end-to-end recipe.
Rubber beam under torsion, compressible Neo-Hookean, L-BFGS load stepping.
Penalty contact between a circular indenter and an elastic block, checked against the Hertz solution.
Plane-strain J2 plasticity with isotropic hardening, load / unload cycle, plus a 3D cube.