solver: J2 plasticity in nonlinear static steps, finite and small strain

Elements of a plastic material take the J2 material point: total Lagrangian
with nonlinear geometry, the small-strain loops without (elastic elements keep
their linear stiffness, so elastic results do not move). The plastic history is
committed per converged increment. Increments follow the step's load path,
ending at its points, the extrapolated predictor scaled by the change of the
load factor. Steps with path-dependent materials start an increment without a
predictor from the tangent predictor (the prescribed motion spread through the
converged tangent), and a first tangent that is not positive definite is a
cutback when the undeformed model's is. Refused by name: the Johnson-Cook rate
term (a static step has no time) and kinematic hardening at finite strain;
damage, erosion and adiabatic heating are left out with a warning. Results
carry the equivalent plastic strain at the integration points (solve.probe,
the step summary). LS-DYNA writes a load path as the step's curve; Abaqus
refuses it and a plastic deck of several general steps (Abaqus carries the
plastic state between them).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

crates/model/src/materials.rs

@@ -1,7 +1,7 @@
 //! Materials: linear elasticity, mass density, fluid behaviour, thermal properties (conductivity,
-//! specific heat, expansion), and the inelastic behaviours of
-//! explicit dynamics: von Mises (J2) plasticity with a bilinear, tabulated or Johnson–Cook flow stress,
-//! Johnson–Cook damage, and element erosion criteria.
+//! specific heat, expansion), and the inelastic behaviours: von Mises (J2) plasticity with a
+//! bilinear, tabulated or Johnson–Cook flow stress (explicit dynamics and nonlinear static
+//! steps), Johnson–Cook damage and element erosion criteria (explicit dynamics).
 //!
 //! The records are solver-neutral and named for what they describe, never after a product's
 //! keyword or material number; the deck writers map them to each format.
@@ -372,8 +372,8 @@ pub struct Material {
     /// How it flows, for fluid domains (needs a density).
     #[serde(default, skip_serializing_if = "Option::is_none")]
     pub fluid: Option<Fluid>,
-    /// Von Mises plasticity (explicit dynamics; the linear implicit solver uses the elastic
-    /// constants alone).
+    /// Von Mises plasticity (explicit dynamics and nonlinear static steps; the linear solvers use
+    /// the elastic constants alone).
     #[serde(default, skip_serializing_if = "Option::is_none")]
     pub plastic: Option<Plastic>,
     /// Damage to failure (explicit dynamics: a failed element erodes).