experimental — computational plasticity under large deformation

Two complementary approaches to 3D computational elastoplasticity, especially at large deformation, live side by side in this repository:

Sub-project	Approach	Status
lagrangian/	Mesh-based finite element method (Lagrangian). Small- and finite-strain J2 plasticity, Hex8 elements, F-bar, CG+AMG scaling to ~10M DOFs.	Complete, tested
particle_method/	Particle / meshfree method (e.g. MPM/SPH) for plasticity under very large deformation, where a fixed mesh distorts and fails.	Exploratory

Why two methods

Mesh-based FEM (the lagrangian/ solver) is accurate and efficient, but a total-Lagrangian formulation is limited by element distortion: at extreme strains (bulk forming, crushing, deformation to fracture) the elements degrade until a Jacobian goes non-positive. Particle / meshfree methods carry the material on points rather than a fixed mesh, so the mesh-distortion barrier disappears — which is why particle_method/ is the natural place to explore the very-large- deformation regime. The two share the same physics (J2 return-mapping constitutive law), so ideas and kernels can cross over.

Getting started

• The finite element solver: see lagrangian/README.md (run examples with julia --project=lagrangian lagrangian/examples/…).
• The particle-method exploration: see particle_method/README.md.