Examples gallery

Every example here is a runnable script in examples/. They share a gen_meshes.py helper that builds the small structured meshes they use.

Run them with uv

All commands assume you've run uv sync --all-packages --all-groups --all-extras first. Prefix everything with uv run.

Canonical: LaTeX → solver

The MVP-stable, documentation-preferred path. Parses % mechanics directives and runs all six layers.

uv run python examples/run_compile_latex.py

See Getting started for a line-by-line walk-through of what this produces.

Programmatic API examples

These build a ProblemIR directly (the secondary, testing-oriented contract surface) and exercise classic FEM verification benchmarks.

Script	What it demonstrates
elastic_cantilever.py	3D SVK cantilever, fixed face + tip traction
cook_membrane.py	Cook's membrane — a standard tapered-panel bending benchmark
necking_bar.py	J2 plasticity necking bar (load–displacement vs. Simo & Hughes)
plastic_uniaxial.py	Uniaxial J2 plasticity stress–strain response
patch_test.py	Constant-strain patch test (must reproduce exactly)
run_pipeline.py	SVK + J2 end-to-end; writes the emitted Taichi source to disk

uv run python examples/elastic_cantilever.py
uv run python examples/cook_membrane.py
uv run python examples/necking_bar.py
uv run python examples/plastic_uniaxial.py
uv run python examples/patch_test.py
uv run python examples/run_pipeline.py

LaTeX energy snippets

The .tex files under examples/ are the exact strain-energy inputs the parser accepts for the derive-from-energy path:

File	Model
svk_energy.tex	St. Venant–Kirchhoff
neo_hookean_energy.tex	Neo-Hookean
mooney_rivlin_energy.tex	Mooney-Rivlin
ogden_energy.tex	Ogden (spectral)
hgo_energy.tex	HGO (fiber-reinforced)

from mechdsl import compile_latex

bundle = compile_latex(problem_source, energy_file="examples/mooney_rivlin_energy.tex")

Cyclic plasticity & the Bauschinger effect

The J2 kinematic and mixed hardening models (mechdsl.lib.plasticity_kinematic / plasticity_mixed) are exercised on a uniaxial cyclic load path (loading → unloading → reverse) in the test suite. The kinematic/mixed models re-yield in reverse below the forward yield magnitude — the Bauschinger effect — which the isotropic model cannot reproduce. The hand-written reference kernels that pin this behaviour are ref_j2_kinematic.py and ref_j2_mixed.py; see the constitutive model catalog for the API.

Verification benchmarks

The verification harness (mechdsl.verify) compares generated output against hand-written reference kernels and analytical solutions. The benchmark suite covers the patch test (exact reproduction), Cook's membrane (within 2% of literature), and the necking bar (load–displacement within 2% of Simo & Hughes 1998). See How it works → verification.