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test: Add finite strain plasticity material model validation
Unit tests for FiniteStrainPlasticity with multiplicative decomposition. Test coverage: - Material construction with validation (E, ν, σ_y, H parameters) - State initialization (F_p, α_bar, κ) - Small strain limit verification - Identity and pure rotation deformation (frame indifference) - Uniaxial extension (elastic and plastic regimes) - Simple shear deformation - Incremental loading with state persistence - Plastic incompressibility constraint (det(F_p) ≈ 1) - Kinematic hardening behavior (backstress evolution) - State persistence across load steps - Type stability verification
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Jukka Aho
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"""
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Unit tests for FiniteStrainPlasticity material model.
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Tests cover:
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1. Construction and validation
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2. State initialization
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3. Small strain limit (should match PerfectPlasticity)
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4. Pure elastic deformation (large rotation)
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5. Uniaxial extension beyond yield
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6. Simple shear
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7. Plastic incompressibility (det(F_p) = 1)
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8. Type stability
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9. State consistency
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"""
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using Test
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using Tensors
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using LinearAlgebra
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# Load implementations
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include("../src/materials/abstract_material.jl")
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include("../src/materials/finite_strain_plasticity.jl")
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@testset "Finite Strain Plasticity Material" begin
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@testset "Material Construction" begin
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# Valid construction
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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@test steel.E == 200e9
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@test steel.ν == 0.3
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@test steel.σ_y == 250e6
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@test steel.H == 1e9
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@test steel.μ ≈ 200e9 / (2 * (1 + 0.3))
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@test steel.λ ≈ 200e9 * 0.3 / ((1 + 0.3) * (1 - 2 * 0.3))
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# Perfect plasticity (H=0)
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perfect = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=0.0)
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@test perfect.H == 0.0
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# Invalid inputs
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@test_throws ArgumentError FiniteStrainPlasticity(E=-200e9, ν=0.3, σ_y=250e6, H=1e9)
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@test_throws ArgumentError FiniteStrainPlasticity(E=200e9, ν=0.6, σ_y=250e6, H=1e9)
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@test_throws ArgumentError FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=-250e6, H=1e9)
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@test_throws ArgumentError FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=-1e9)
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end
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@testset "State Construction" begin
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# Default state (identity F_p)
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state0 = FiniteStrainPlasticityState()
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@test state0.F_p == one(Tensor{2,3})
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@test state0.α_bar == zero(SymmetricTensor{2,3})
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@test state0.κ == 0.0
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@test det(state0.F_p) ≈ 1.0
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# Custom state
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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))
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F_p = F_p / det(F_p)^(1 / 3) # Enforce det = 1
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α_bar = SymmetricTensor{2,3}((1e8, 0.0, 0.0, 0.0, 0.0, 0.0))
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state = FiniteStrainPlasticityState(F_p, α_bar, 0.01)
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@test state.F_p ≈ F_p
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@test state.α_bar == α_bar
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@test state.κ == 0.01
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# Invalid state (negative κ)
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@test_throws ArgumentError FiniteStrainPlasticityState(F_p, α_bar, -0.01)
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end
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@testset "Small Strain Limit" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Small deformation: F ≈ I + ∇u
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ε_small = 1e-5
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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))
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σ, 𝔸, state = compute_stress(steel, F_small, nothing, 0.0)
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# Should remain elastic
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@test state.F_p ≈ one(Tensor{2,3})
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@test state.α_bar == zero(SymmetricTensor{2,3})
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@test state.κ == 0.0
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# Stress should be small
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@test norm(σ) < 1e6 # Less than 1 MPa
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end
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@testset "Identity Deformation" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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F_identity = one(Tensor{2,3})
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σ, 𝔸, state = compute_stress(steel, F_identity, nothing, 0.0)
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# Zero stress for no deformation
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@test norm(σ) < 1e-10
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@test state.F_p == one(Tensor{2,3})
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@test state.κ == 0.0
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end
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@testset "Pure Rotation (Elastic)" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# 45-degree rotation around z-axis (no stretching)
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θ = π / 4
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c = cos(θ)
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s = sin(θ)
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R = Tensor{2,3}((c, s, 0.0, -s, c, 0.0, 0.0, 0.0, 1.0))
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σ, 𝔸, state = compute_stress(steel, R, nothing, 0.0)
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# Pure rotation should give zero stress (if formulation is objective)
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# Note: May not be exactly zero due to numerical precision
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@test norm(σ) < 1e6 # Should be small
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@test state.F_p ≈ one(Tensor{2,3}) rtol = 1e-6
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end
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@testset "Uniaxial Extension (Elastic)" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# 1% extension in x-direction
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λ = 1.01
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F_ext = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ, 𝔸, state = compute_stress(steel, F_ext, nothing, 0.0)
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# Should remain elastic (small extension)
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@test state.F_p ≈ one(Tensor{2,3}) rtol = 1e-6
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@test state.κ == 0.0
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# Check that σ_xx > 0 (tension)
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@test σ[1, 1] > 0.0
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end
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@testset "Uniaxial Extension (Plastic)" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Large extension (10%)
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λ = 1.10
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F_ext = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ, 𝔸, state = compute_stress(steel, F_ext, nothing, 0.0)
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# Should have plastic deformation
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@test norm(state.F_p - one(Tensor{2,3})) > 1e-6
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@test state.κ > 0.0
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# Plastic incompressibility: det(F_p) ≈ 1
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@test abs(det(state.F_p) - 1.0) < 1e-3
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end
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@testset "Simple Shear" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Shear deformation: γ = 0.1
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γ = 0.1
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F_shear = Tensor{2,3}((1.0, γ, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ, 𝔸, state = compute_stress(steel, F_shear, nothing, 0.0)
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# Check shear stress exists
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@test abs(σ[1, 2]) > 0.0
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# det(F) should be 1 for simple shear
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@test abs(det(F_shear) - 1.0) < 1e-10
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end
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@testset "Incremental Loading" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Load in increments
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n_steps = 5
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λ_max = 1.05
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state = FiniteStrainPlasticityState()
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stresses = Float64[]
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plastic_strains = Float64[]
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for i in 1:n_steps
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λ = 1.0 + (λ_max - 1.0) * i / n_steps
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F = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ, 𝔸, state = compute_stress(steel, F, state, 0.0)
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push!(stresses, σ[1, 1])
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push!(plastic_strains, state.κ)
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end
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# Stress should increase (with hardening)
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@test all(diff(stresses) .≥ -1e-6) # Allow small numerical errors
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# Plastic strain should increase monotonically
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@test all(diff(plastic_strains) .≥ 0.0)
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end
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@testset "Plastic Incompressibility" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Various deformation levels
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stretches = [1.02, 1.05, 1.10, 1.15, 1.20]
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for λ in stretches
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F = Tensor{2,3}((λ, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ, 𝔸, state = compute_stress(steel, F, nothing, 0.0)
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# Check plastic incompressibility
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det_Fp = det(state.F_p)
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@test abs(det_Fp - 1.0) < 0.01 # Within 1% (relaxed due to exponential map approximation)
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end
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end
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@testset "Hardening Behavior" begin
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steel_hard = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=10e9)
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steel_perf = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=0.0)
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F_test = Tensor{2,3}((1.08, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ_hard, _, state_hard = compute_stress(steel_hard, F_test, nothing, 0.0)
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σ_perf, _, state_perf = compute_stress(steel_perf, F_test, nothing, 0.0)
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# Hardening material should have higher stress
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@test σ_hard[1, 1] > σ_perf[1, 1]
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# Hardening material should have backstress
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@test norm(state_hard.α_bar) > 0.0
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@test norm(state_perf.α_bar) == 0.0
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end
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@testset "State Persistence" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# First load
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F1 = Tensor{2,3}((1.08, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ1, _, state1 = compute_stress(steel, F1, nothing, 0.0)
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# Unload to smaller deformation
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F2 = Tensor{2,3}((1.02, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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σ2, _, state2 = compute_stress(steel, F2, state1, 0.0)
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# Plastic strain should not decrease
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@test state2.κ ≥ state1.κ
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# F_p should not go back to identity
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@test norm(state2.F_p - one(Tensor{2,3})) > 1e-6
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end
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@testset "Simplified Interface" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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F = Tensor{2,3}((1.05, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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# Test with and without explicit state/Δt
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σ1, 𝔸1, state1 = compute_stress(steel, F)
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σ2, 𝔸2, state2 = compute_stress(steel, F, nothing, 0.0)
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@test σ1 ≈ σ2
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@test state1.κ ≈ state2.κ
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end
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@testset "Type Stability" begin
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steel = FiniteStrainPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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F = Tensor{2,3}((1.05, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0))
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state = FiniteStrainPlasticityState()
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# Infer return types
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result = @inferred compute_stress(steel, F, state, 0.0)
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@test result isa Tuple{SymmetricTensor{2,3,Float64},
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SymmetricTensor{4,3,Float64},
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FiniteStrainPlasticityState}
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end
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end
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