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/fem/src/lib.rs

@@ -14,12 +14,13 @@
 //!   the solid kernels evaluate;
 //! - [`material`]: isotropic and orthotropic elasticity matrices, von Mises stress;
 //! - [`constitutive`]: the material point of finite-strain analysis (Kirchhoff stress and
-//!   spatial tangent from the deformation gradient, with history): St Venant–Kirchhoff and
-//!   neo-Hookean;
+//!   spatial tangent from the deformation gradient, with history): St Venant–Kirchhoff,
+//!   neo-Hookean and J2 plasticity;
 //! - [`element`]: the element table, stiffness (full, reduced, incompatible modes), consistent
 //!   and lumped mass, body forces, integration-point stresses and their extrapolation to nodes;
 //! - [`finite`]: total Lagrangian solid and 2D elements (internal forces, the consistent tangent
-//!   with its geometric part, mixed u–p at finite strain, Cauchy stress and logarithmic strain);
+//!   with its geometric part, mixed u–p at finite strain, Cauchy stress and logarithmic strain),
+//!   and the same with small strain for inelastic materials;
 //! - [`plane`]: 2D elements (plane stress, plane strain, axisymmetric) on tri3, tri6, quad4 and
 //!   quad8, with two displacement components per node;
 //! - [`shell`]: flat MITC4 quadrilateral and MITC3 triangle shells with a drilling rotation, six
@@ -33,6 +34,9 @@
 //!   shape vectors and element frequency bounds for explicit dynamics;
 //! - [`rotation`]: incrementally objective stress updates (Hughes–Winget Jaumann, Flanagan–Taylor
 //!   Green–Naghdi);
+//! - [`elastoplastic`]: J2 plasticity at a material point of implicit analysis, at finite strain
+//!   (Simo's exponential map in the principal logarithmic strains) and at small strain, with the
+//!   consistent tangents, on the radial return of [`plasticity`];
 //! - [`plasticity`]: J2 radial return with isotropic, kinematic and Johnson–Cook hardening,
 //!   Johnson–Cook damage;
 //! - [`truss`]: two- and three-node trusses (straight or curved), their stiffness, mass, body
@@ -52,6 +56,7 @@ pub mod beam;
 pub mod constitutive;
 pub mod dense;
 pub mod dof;
+pub mod elastoplastic;
 pub mod element;
 pub mod face;
 pub mod finite;