fem: J2 plasticity at the implicit material point, finite and small strain

The radial return of the explicit update is now J2::radial_return, called by
both solvers, with the consistent tangent J2::tangent (Simo & Hughes 1998,
Box 3.2). The new elastoplastic module gives the implicit material point:
Simo's multiplicative plasticity with the exponential return map in the
principal logarithmic strains (CMAME 99, 1992) and its spatial tangent through
the Daleckii-Krein divided differences of the logarithm, and the additive
radial return of small strain with kinematic hardening. MaterialModel::Plastic
carries it, decoupled (deviatoric return, Hencky volume) so hybrid elements
take it. The element loops of finite.rs gain small-strain kinematics for
inelastic materials and pass history through the mixed path. Every tangent is
checked against central differences, element by element, from a plastic
history.

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

crates/solver/src/nonlinear.rs

@@ -62,6 +62,7 @@
 use fieldcraft_fem::constitutive::MaterialModel;
 use fieldcraft_fem::dense::Matrix;
 use fieldcraft_fem::element::{Extrapolation, extrapolation};
+use fieldcraft_fem::finite::Kinematics;
 use fieldcraft_fem::quadrature::Rule;
 use fieldcraft_fem::{DofKind, DofSet, ElementType, PointStress, face, von_mises};
 use fieldcraft_model::{Extent, Load, Model, NonlinearStatic, Procedure, Step};
@@ -250,7 +251,7 @@ impl Problem<'_> {
         }
         let material = self.materials.get(e).ok_or_else(|| Error::Internal("element material".into()))?;
         let mut updated = committed.to_vec();
-        let r = kernel.finite_strain(material, &ue, committed, &mut updated, tangent).map_err(at)?;
+        let r = kernel.nonlinear(material, &ue, Kinematics::Finite, committed, &mut updated, tangent).map_err(at)?;
         Ok((r.force, r.tangent, updated))
     }
 
@@ -833,7 +834,7 @@ fn finish(
         let kernel = el.kernel()?;
         let points = if problem.finite {
             let material = problem.materials.get(i).ok_or_else(|| Error::Internal("element material".into()))?;
-            kernel.finite_strain_stresses(material, &ue, committed.get(i).map(Vec::as_slice).unwrap_or_default())
+            kernel.nonlinear_stresses(material, &ue, Kinematics::Finite, committed.get(i).map(Vec::as_slice).unwrap_or_default())
         } else {
             let per_node: Vec<[f64; 3]> = el.nodes.iter().map(|n| displacement.get(*n).copied().unwrap_or_default()).collect();
             kernel.stresses_with(&el.d, &per_node, None)

crates/solver/src/system.rs

@@ -11,6 +11,7 @@ use fieldcraft_fem::beam::{Beam, BeamSection};
 use fieldcraft_fem::constitutive::MaterialModel;
 use fieldcraft_fem::dense::Matrix;
 use fieldcraft_fem::element::{Formulation, Solid, ThermalStrain};
+use fieldcraft_fem::finite::Kinematics;
 use fieldcraft_fem::plane::{Plane, Theory};
 use fieldcraft_fem::shell::{Shell, ShellSection};
 use fieldcraft_fem::truss::{Truss, young_modulus};
@@ -113,27 +114,30 @@ impl Kernel<'_> {
         }
     }
 
-    /// Finite-strain internal forces and tangent ([`fieldcraft_fem::finite`]) for the element's
-    /// displacements `u` (its degrees of freedom in order: 3 per node, or 2 for 2D elements).
-    pub fn finite_strain(
+    /// Nonlinear internal forces and tangent ([`fieldcraft_fem::finite`]) for the element's
+    /// displacements `u` (its degrees of freedom in order: 3 per node, or 2 for 2D elements),
+    /// total Lagrangian or with small strain.
+    pub fn nonlinear(
         &self,
         m: &MaterialModel,
         u: &[f64],
+        kin: Kinematics,
         committed: &[f64],
         updated: &mut [f64],
         tangent: bool,
     ) -> fieldcraft_fem::Result<fieldcraft_fem::finite::Finite> {
         match self {
-            Kernel::Solid(s) => s.finite_strain(m, u.as_chunks::<3>().0, committed, updated, tangent),
-            Kernel::Plane(p) => p.finite_strain(m, u.as_chunks::<2>().0, committed, updated, tangent),
+            Kernel::Solid(s) => s.nonlinear(m, u.as_chunks::<3>().0, kin, committed, updated, tangent),
+            Kernel::Plane(p) => p.nonlinear(m, u.as_chunks::<2>().0, kin, committed, updated, tangent),
         }
     }
 
-    /// Cauchy stress and logarithmic strain at the integration points, as [`Self::finite_strain`].
-    pub fn finite_strain_stresses(&self, m: &MaterialModel, u: &[f64], committed: &[f64]) -> fieldcraft_fem::Result<Vec<PointStress>> {
+    /// Cauchy stress and strain (logarithmic at finite strain) at the integration points, as
+    /// [`Self::nonlinear`].
+    pub fn nonlinear_stresses(&self, m: &MaterialModel, u: &[f64], kin: Kinematics, committed: &[f64]) -> fieldcraft_fem::Result<Vec<PointStress>> {
         match self {
-            Kernel::Solid(s) => s.finite_strain_stresses(m, u.as_chunks::<3>().0, committed),
-            Kernel::Plane(p) => p.finite_strain_stresses(m, u.as_chunks::<2>().0, committed),
+            Kernel::Solid(s) => s.nonlinear_stresses(m, u.as_chunks::<3>().0, kin, committed),
+            Kernel::Plane(p) => p.nonlinear_stresses(m, u.as_chunks::<2>().0, kin, committed),
         }
     }