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+"""
+# Unit Tests: Finite Strain Plasticity (Multiplicative Decomposition)
+
+**What:** Comprehensive validation of finite strain J2 plasticity with F = F_e F_p decomposition
+
+**Why:**
+- Geometrically exact plasticity for large deformations (>10% strain)
+- Tests multiplicative decomposition F = F_e F_p (not additive ε = ε_e + ε_p)
+- Validates plastic incompressibility det(F_p) = 1 (fundamental constraint)
+- Critical for metal forming, impact, crashworthiness (extreme deformations)
+- Demonstrates objective stress update (rotation-independent)
+
+**How:**
+Test suite validates:
+1. **Construction & parameters** - E, ν, σ_y, H validity, computed μ and λ
+2. **State management** - FiniteStrainPlasticityState(F_p, α_bar, κ) with F_p=I default
+3. **Small strain limit** - Should recover small-strain plasticity for F ≈ I + ∇u
+4. **Identity deformation** - F = I gives σ = 0, F_p = I, κ = 0
+5. **Pure rotation** - Rigid body rotation (no stretch) should give σ ≈ 0 (objectivity)
+6. **Uniaxial extension** - Elastic (λ=1.01) and plastic (λ=1.10) regimes
+7. **Simple shear** - Validates shear response, det(F) = 1
+8. **Incremental loading** - Monotonic loading: stress and κ increase
+9. **Plastic incompressibility** - det(F_p) ≈ 1 for all stretches λ ∈ [1.02, 1.20]
+10. **Hardening behavior** - H > 0: higher stress, backstress α_bar ≠ 0
+11. **State persistence** - Unloading: plastic strain κ does not decrease
+12. **Performance** - Type stability
+
+**Mathematical Background:**
+- Multiplicative decomposition: F = F_e F_p (Lee decomposition)
+  - F: Total deformation gradient
+  - F_e: Elastic part (recoverable on unloading)
+  - F_p: Plastic part (permanent deformation)
+- Plastic incompressibility: det(F_p) = 1 (volume preservation in plastic flow)
+- Mandel stress: M = C_e S_e (intermediate configuration)
+- Yield criterion: f = √(3/2·dev(M):dev(M)) - σ_y ≤ 0 (von Mises)
+- Flow rule: Ḟ_p F_p⁻¹ = Δγ·n (exponential map integration)
+- Hardening: α̇_bar = H·ε̇_p (backstress evolution in intermediate config)
+- Objectivity: σ(Q·F) = Q·σ(F)·Q^T for rotation Q (frame-invariance)
+- Physical constraints: det(F) > 0, det(F_e) > 0, det(F_p) = 1
+
+**Expected Results:**
+✅ Material constructed: E=200 GPa, ν=0.3, σ_y=250 MPa, H=0-10 GPa
+✅ Perfect plasticity: H=0 valid
+✅ Invalid inputs rejected: E<0, ν>0.5, σ_y<0, H<0, κ<0
+✅ Default state: F_p=I (det=1), α_bar=0, κ=0
+✅ Small strain (ε=1e-5): F_p≈I, κ=0, ||σ|| < 1 MPa
+✅ Identity (F=I): σ=0 exactly
+✅ Pure rotation (45° around z): ||σ|| < 1 MPa (objectivity), F_p≈I
+✅ Uniaxial elastic (λ=1.01): F_p≈I, κ=0, σ_xx > 0
+✅ Uniaxial plastic (λ=1.10): ||F_p-I|| > 1e-6, κ > 0, |det(F_p)-1| < 0.001
+✅ Simple shear (γ=0.1): σ_xy ≠ 0, det(F)=1
+✅ Incremental (5 steps to λ=1.05): Monotonic stress and κ
+✅ Incompressibility: |det(F_p)-1| < 0.01 for λ ∈ [1.02,1.20]
+✅ Hardening: H=10 GPa → σ > σ_perfect, ||α_bar|| > 0
+✅ State persistence: Load λ=1.08 then unload λ=1.02 → κ doesn't decrease
+✅ Simplified interface (without state, Δt) matches full call
+✅ Type-stable: returns Tuple{SymmetricTensor{2,3}, SymmetricTensor{4,3}, FiniteStrainPlasticityState}
+
+**Test Coverage:**
+- 14 test sets, ~70 individual assertions
+- Material constants: Steel (E=200 GPa, ν=0.3, σ_y=250 MPa, H=0-10 GPa)
+- Deformations: Identity, small (ε=1e-5), rotation (45°), uniaxial (λ=1.01-1.20), shear (γ=0.1)
+- Validation methods: Plastic incompressibility, objectivity, state persistence, hardening comparison
+- Algorithms: Multiplicative decomposition, exponential map, return mapping in intermediate config
+- Edge cases: Perfect plasticity (H=0), pure rotation, incremental loading, unloading
+
+**Key Physics:**
+- Multiplicative decomposition: Geometrically exact (not linearized)
+- Plastic incompressibility: Fundamental for metals (no volume change in plastic flow)
+- Objectivity: Stress independent of observer reference frame (essential for large rotations)
+- Lee decomposition: Separates elastic (lattice stretch) from plastic (slip) deformations
+- Intermediate configuration: Where plasticity lives (stress-free but plastically deformed)
+- Exponential map: Preserves det(F_p) = 1 during integration (unlike additive schemes)
+"""
+
+using Test
+using Tensors
+using LinearAlgebra
+
+# Load implementations
+include("../src/materials/abstract_material.jl")
+include("../src/materials/finite_strain_plasticity.jl")
+
+@testset "Finite Strain Plasticity Material" begin
+
+    @testset "Material Construction" begin
+        # Valid construction
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+        @test steel.E == 200e9
+        @test steel.ν == 0.3
+        @test steel.σ_y == 250e6
+        @test steel.H == 1e9
+        @test steel.μ ≈ 200e9 / (2 * (1 + 0.3))
+        @test steel.λ ≈ 200e9 * 0.3 / ((1 + 0.3) * (1 - 2 * 0.3))
+
+        # Perfect plasticity (H=0)
+        perfect = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=0.0)
+        @test perfect.H == 0.0
+
+        # Invalid inputs
+        @test_throws ArgumentError FiniteStrainPlasticity(E=-200e9, ν=0.3, σ_y=250e6, H=1e9)
+        @test_throws ArgumentError FiniteStrainPlasticity(E=200e9, ν=0.6, σ_y=250e6, H=1e9)
+        @test_throws ArgumentError FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=-250e6, H=1e9)
+        @test_throws ArgumentError FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=-1e9)
+    end
+
+    @testset "State Construction" begin
+        # Default state (identity F_p)
+        state0 = FiniteStrainPlasticityState()
+        @test state0.F_p == one(Tensor{2,3})
+        @test state0.α_bar == zero(SymmetricTensor{2,3})
+        @test state0.κ == 0.0
+        @test det(state0.F_p) ≈ 1.0
+
+        # Custom state
+        F_p = one(Tensor{2,3}) + 0.01 * Tensor{2,3}((0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0))
+        F_p = F_p / det(F_p)^(1 / 3)  # Enforce det = 1
+        α_bar = SymmetricTensor{2,3}((1e8, 0.0, 0.0, 0.0, 0.0, 0.0))
+        state = FiniteStrainPlasticityState(F_p, α_bar, 0.01)
+        @test state.F_p ≈ F_p
+        @test state.α_bar == α_bar
+        @test state.κ == 0.01
+
+        # Invalid state (negative κ)
+        @test_throws ArgumentError FiniteStrainPlasticityState(F_p, α_bar, -0.01)
+    end
+
+    @testset "Small Strain Limit" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # Small deformation: F ≈ I + ∇u
+        ε_small = 1e-5
+        F_small = one(Tensor{2,3}) + ε_small * Tensor{2,3}((1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0))
+
+        σ, 𝔸, state = compute_stress(steel, F_small, nothing, 0.0)
+
+        # Should remain elastic
+        @test state.F_p ≈ one(Tensor{2,3})
+        @test state.α_bar == zero(SymmetricTensor{2,3})
+        @test state.κ == 0.0
+
+        # Stress should be small
+        @test norm(σ) < 1e6  # Less than 1 MPa
+    end
+
+    @testset "Identity Deformation" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+        F_identity = one(Tensor{2,3})
+
+        σ, 𝔸, state = compute_stress(steel, F_identity, nothing, 0.0)
+
+        # Zero stress for no deformation
+        @test norm(σ) < 1e-10
+        @test state.F_p == one(Tensor{2,3})
+        @test state.κ == 0.0
+    end
+
+    @testset "Pure Rotation (Elastic)" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # 45-degree rotation around z-axis (no stretching)
+        θ = π / 4
+        c = cos(θ)
+        s = sin(θ)
+        R = Tensor{2,3}((c, s, 0.0, -s, c, 0.0, 0.0, 0.0, 1.0))
+
+        σ, 𝔸, state = compute_stress(steel, R, nothing, 0.0)
+
+        # Pure rotation should give zero stress (if formulation is objective)
+        # Note: May not be exactly zero due to numerical precision
+        @test norm(σ) < 1e6  # Should be small
+        @test state.F_p ≈ one(Tensor{2,3}) rtol = 1e-6
+    end
+
+    @testset "Uniaxial Extension (Elastic)" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # 1% extension in x-direction
+        λ = 1.01
+        F_ext = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+
+        σ, 𝔸, state = compute_stress(steel, F_ext, nothing, 0.0)
+
+        # Should remain elastic (small extension)
+        @test state.F_p ≈ one(Tensor{2,3}) rtol = 1e-6
+        @test state.κ == 0.0
+
+        # Check that σ_xx > 0 (tension)
+        @test σ[1, 1] > 0.0
+    end
+
+    @testset "Uniaxial Extension (Plastic)" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # Large extension (10%)
+        λ = 1.10
+        F_ext = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+
+        σ, 𝔸, state = compute_stress(steel, F_ext, nothing, 0.0)
+
+        # Should have plastic deformation
+        @test norm(state.F_p - one(Tensor{2,3})) > 1e-6
+        @test state.κ > 0.0
+
+        # Plastic incompressibility: det(F_p) ≈ 1
+        @test abs(det(state.F_p) - 1.0) < 1e-3
+    end
+
+    @testset "Simple Shear" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # Shear deformation: γ = 0.1
+        γ = 0.1
+        F_shear = Tensor{2,3}((1.0, γ, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+
+        σ, 𝔸, state = compute_stress(steel, F_shear, nothing, 0.0)
+
+        # Check shear stress exists
+        @test abs(σ[1, 2]) > 0.0
+
+        # det(F) should be 1 for simple shear
+        @test abs(det(F_shear) - 1.0) < 1e-10
+    end
+
+    @testset "Incremental Loading" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # Load in increments
+        n_steps = 5
+        λ_max = 1.05
+
+        state = FiniteStrainPlasticityState()
+        stresses = Float64[]
+        plastic_strains = Float64[]
+
+        for i in 1:n_steps
+            λ = 1.0 + (λ_max - 1.0) * i / n_steps
+            F = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+            σ, 𝔸, state = compute_stress(steel, F, state, 0.0)
+
+            push!(stresses, σ[1, 1])
+            push!(plastic_strains, state.κ)
+        end
+
+        # Stress should increase (with hardening)
+        @test all(diff(stresses) .≥ -1e-6)  # Allow small numerical errors
+
+        # Plastic strain should increase monotonically
+        @test all(diff(plastic_strains) .≥ 0.0)
+    end
+
+    @testset "Plastic Incompressibility" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # Various deformation levels
+        stretches = [1.02, 1.05, 1.10, 1.15, 1.20]
+
+        for λ in stretches
+            F = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+            σ, 𝔸, state = compute_stress(steel, F, nothing, 0.0)
+
+            # Check plastic incompressibility
+            det_Fp = det(state.F_p)
+            @test abs(det_Fp - 1.0) < 0.01  # Within 1% (relaxed due to exponential map approximation)
+        end
+    end
+
+    @testset "Hardening Behavior" begin
+        steel_hard = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=10e9)
+        steel_perf = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=0.0)
+
+        F_test = Tensor{2,3}((1.08, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+
+        σ_hard, _, state_hard = compute_stress(steel_hard, F_test, nothing, 0.0)
+        σ_perf, _, state_perf = compute_stress(steel_perf, F_test, nothing, 0.0)
+
+        # Hardening material should have higher stress
+        @test σ_hard[1, 1] > σ_perf[1, 1]
+
+        # Hardening material should have backstress
+        @test norm(state_hard.α_bar) > 0.0
+        @test norm(state_perf.α_bar) == 0.0
+    end
+
+    @testset "State Persistence" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+
+        # First load
+        F1 = Tensor{2,3}((1.08, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+        σ1, _, state1 = compute_stress(steel, F1, nothing, 0.0)
+
+        # Unload to smaller deformation
+        F2 = Tensor{2,3}((1.02, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+        σ2, _, state2 = compute_stress(steel, F2, state1, 0.0)
+
+        # Plastic strain should not decrease
+        @test state2.κ ≥ state1.κ
+
+        # F_p should not go back to identity
+        @test norm(state2.F_p - one(Tensor{2,3})) > 1e-6
+    end
+
+    @testset "Simplified Interface" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+        F = Tensor{2,3}((1.05, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+
+        # Test with and without explicit state/Δt
+        σ1, 𝔸1, state1 = compute_stress(steel, F)
+        σ2, 𝔸2, state2 = compute_stress(steel, F, nothing, 0.0)
+
+        @test σ1 ≈ σ2
+        @test state1.κ ≈ state2.κ
+    end
+
+    @testset "Type Stability" begin
+        steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
+        F = Tensor{2,3}((1.05, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
+        state = FiniteStrainPlasticityState()
+
+        # Infer return types
+        result = @inferred compute_stress(steel, F, state, 0.0)
+
+        @test result isa Tuple{SymmetricTensor{2,3,Float64},
+            SymmetricTensor{4,3,Float64},
+            FiniteStrainPlasticityState}
+    end
+
+end