feat(materials): add St. Venant–Kirchhoff J2 finite-strain plasticity

Combine Green–Lagrange kinematics with J₂ return mapping on the elastic predictor.

- Override `continuum_kinematics` and declare required IP state variables.

src/materials/stvenant_kirchhoff_j2.jl

@@ -0,0 +1,96 @@
+# SPDX-FileCopyrightText: 2015-2026 Jukka Aho
+# SPDX-License-Identifier: MIT
+
+"""
+J₂ plasticity with a **St. Venant–Kirchhoff** elastic relation written on the
+Green–Lagrange strain `E` from the assembly (`update_material_cache!` uses
+[`GreenLagrangeKinematics`](@ref)).
+
+This is **not** multiplicative finite-strain plasticity; it is the common
+total-Lagrangian approximation that keeps the same radial return as
+[`PerfectPlasticity`](@ref) but replaces small-strain `ε` with `E`.
+
+See [`continuum_kinematics`](@ref).
+"""
+
+using Tensors
+
+struct StVenantKirchhoffJ2Plasticity <: AbstractPlasticMaterial
+    E::Float64
+    ν::Float64
+    σ_y::Float64
+    H::Float64
+    μ::Float64
+    λ::Float64
+
+    function StVenantKirchhoffJ2Plasticity(E::Float64, ν::Float64, σ_y::Float64, H::Float64)
+        E > 0.0 || throw(ArgumentError("Young's modulus must be positive"))
+        -1.0 < ν < 0.5 || throw(ArgumentError("Poisson's ratio out of range"))
+        σ_y > 0.0 || throw(ArgumentError("Yield stress must be positive"))
+        H ≥ 0.0 || throw(ArgumentError("Hardening modulus must be non-negative"))
+        μ = E / (2(1 + ν))
+        λ = E * ν / ((1 + ν) * (1 - 2ν))
+        new(E, ν, σ_y, H, μ, λ)
+    end
+end
+
+StVenantKirchhoffJ2Plasticity(; E::Real, ν::Real, σ_y::Real, H::Real) =
+    StVenantKirchhoffJ2Plasticity(Float64(E), Float64(ν), Float64(σ_y), Float64(H))
+
+material_behavior(::StVenantKirchhoffJ2Plasticity) = StatefulStrainDependent()
+supported_physics(::StVenantKirchhoffJ2Plasticity) = (Elasticity{3}(),)
+required_state_variables(::StVenantKirchhoffJ2Plasticity) =
+    (PlasticStrain, Backstress, EquivalentPlasticStrain)
+
+continuum_kinematics(::StVenantKirchhoffJ2Plasticity) = GreenLagrangeKinematics()
+
+function compute_stress(
+    m::StVenantKirchhoffJ2Plasticity,
+    Estrain::SymmetricTensor{2,3},
+    ::Nothing,
+    Δt::Float64,
+)
+    return compute_stress(m, Estrain, NamedTuple(), Δt)
+end
+
+function compute_stress(
+    m::StVenantKirchhoffJ2Plasticity,
+    Estrain::SymmetricTensor{2,3},
+    state_old::NamedTuple,
+    Δt::Float64,
+)
+    μ = m.μ
+    λ = m.λ
+    σ_y = m.σ_y
+    H = m.H
+
+    ε_p_old = get(state_old, :ε_p, zero(SymmetricTensor{2,3}))
+    α_old = get(state_old, :α, zero(SymmetricTensor{2,3}))
+    κ_old = get(state_old, :κ, 0.0)
+
+    ε_e = Estrain - ε_p_old
+    I = one(Estrain)
+    σ_trial = λ * tr(ε_e) * I + 2μ * ε_e
+
+    s_trial = dev(σ_trial - α_old)
+    s_trial_norm = √(3 / 2) * √(s_trial ⊡ s_trial)
+    f_trial = s_trial_norm - σ_y
+
+    if f_trial ≤ 0.0
+        σ = σ_trial
+        state_new = (ε_p=ε_p_old, α=α_old, κ=κ_old)
+        𝔻 = λ * I ⊗ I + 2μ * symmetric_identity_tensor()
+    else
+        n = s_trial / s_trial_norm
+        Δλ = f_trial / (2μ + (2.0 / 3.0) * H)
+        σ = σ_trial - 2μ * Δλ * n
+        α_new = α_old + (2.0 / 3.0) * H * Δλ * n
+        ε_p_new = ε_p_old + Δλ * n
+        κ_new = κ_old + Δλ
+        state_new = (ε_p=ε_p_new, α=α_new, κ=κ_new)
+        𝔻_e = λ * I ⊗ I + 2μ * symmetric_identity_tensor()
+        𝔻 = 𝔻_e - (4μ^2 / (2μ + (2.0 / 3.0) * H)) * (n ⊗ n)
+    end
+
+    return σ, 𝔻, state_new
+end