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refactor(materials): streamline perfect plasticity documentation
Removed verbose documentation sections: - Removed extensive theory documentation (yield function, flow rule, hardening law, consistency condition) - Removed detailed algorithm step-by-step explanations (radial return mapping) - Removed type hierarchy, construction examples, and derived properties - Removed performance notes and timing information - Removed detailed function documentation with algorithm steps Simplified docstrings to essential information about material parameters and function signatures.
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Jukka Aho
@@ -1,88 +1,7 @@
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"""
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Perfect Plasticity Material (J2 Plasticity with Kinematic Hardening)
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Classical von Mises plasticity with:
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- Small strain formulation
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- Associative flow rule (normality)
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- Radial return mapping algorithm
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- Kinematic hardening (backstress evolution)
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Reference:
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- Simo & Hughes (1998) - "Computational Inelasticity"
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- De Souza Neto et al. (2008) - "Computational Methods for Plasticity"
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Theory
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======
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Yield Function (von Mises):
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f = √(3/2)||dev(σ - α)|| - σ_y
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Where:
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σ - Cauchy stress tensor
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α - Backstress (kinematic hardening)
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σ_y - Yield stress
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dev(·) - Deviatoric part
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Elastic Domain:
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f ≤ 0 → Elastic behavior
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f > 0 → Plastic loading (return to surface)
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Flow Rule (Associative):
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dε^p = dλ · ∂f/∂σ = dλ · n
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Where:
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n = √(3/2) · dev(σ - α) / ||dev(σ - α)|| (flow direction)
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dλ - Plastic multiplier
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Hardening Law (Kinematic):
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dα = (2/3) H · dε^p
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Where:
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H - Hardening modulus
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Consistency Condition:
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f = 0 during plastic loading
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df = 0 (stress remains on yield surface)
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Algorithm
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=========
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Radial Return Mapping (closest point projection):
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1. Elastic Predictor:
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σ_trial = σ_n + 𝔻 : Δε
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2. Check Yield:
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f_trial = √(3/2)||dev(σ_trial - α_n)|| - σ_y
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3a. If f_trial ≤ 0: ELASTIC
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σ_{n+1} = σ_trial
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α_{n+1} = α_n
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ε^p_{n+1} = ε^p_n
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3b. If f_trial > 0: PLASTIC
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Solve for plastic multiplier Δλ:
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f(σ_trial - 2μΔλ·n - (2/3)HΔλ·n, α_n + (2/3)HΔλ·n) = 0
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Update state:
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n = dev(σ_trial - α_n) / ||dev(σ_trial - α_n)||
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Δλ = (f_trial) / (3μ + H)
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σ_{n+1} = σ_trial - 2μΔλ·n
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α_{n+1} = α_n + (2/3)HΔλ·n
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ε^p_{n+1} = ε^p_n + Δλ·n
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4. Consistent Tangent:
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𝔻^ep = 𝔻 - (4μ²/(3μ+H)) · (n ⊗ n)
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Performance
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===========
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Expected: ~10-20× slower than LinearElastic due to:
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- State updates (memory writes)
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- Conditional logic (elastic vs plastic)
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- Tensor deviatoric decomposition
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But still fast: ~200-500 ns per evaluation
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Classical von Mises plasticity with radial return mapping algorithm.
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"""
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using Tensors
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@@ -105,32 +24,6 @@ J2 (von Mises) plasticity with kinematic hardening.
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- `ν::Float64` - Poisson's ratio [-]
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- `σ_y::Float64` - Yield stress [Pa]
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- `H::Float64` - Hardening modulus [Pa]
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# Derived Properties
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- `μ = E/(2(1+ν))` - Shear modulus
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- `λ = Eν/((1+ν)(1-2ν))` - Lamé parameter
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# Type Hierarchy
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`PerfectPlasticity <: AbstractPlasticMaterial <: AbstractMaterial`
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# Construction
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```julia
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# Basic construction
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steel = PerfectPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Perfect plasticity (no hardening)
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steel_perfect = PerfectPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=0.0)
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```
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# Theory
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Classical J2 plasticity:
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- von Mises yield criterion
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- Associative flow rule (normality)
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- Kinematic hardening (backstress evolution)
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- Radial return mapping
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# Performance
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~200-500 ns per evaluation (10-20× slower than LinearElastic)
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"""
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struct PerfectPlasticity <: AbstractPlasticMaterial
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E::Float64 # Young's modulus [Pa]
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@@ -161,21 +54,6 @@ end
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PerfectPlasticity(; E, ν, σ_y, H)
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Keyword constructor for perfect plasticity material.
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# Arguments
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- `E::Real` - Young's modulus [Pa]
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- `ν::Real` - Poisson's ratio [-], must satisfy -1 < ν < 0.5
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- `σ_y::Real` - Yield stress [Pa]
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- `H::Real` - Hardening modulus [Pa] (H=0 for perfect plasticity)
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# Example
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```julia
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# Linear hardening
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steel = PerfectPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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# Perfect plasticity (no hardening)
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steel_perfect = PerfectPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=0.0)
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```
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"""
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PerfectPlasticity(; E::Real, ν::Real, σ_y::Real, H::Real) =
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PerfectPlasticity(Float64(E), Float64(ν), Float64(σ_y), Float64(H))
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@@ -191,37 +69,9 @@ supported_physics(::PerfectPlasticity) = (Elasticity{3}(),)
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required_state_variables(::PerfectPlasticity) = (PlasticStrain, Backstress, EquivalentPlasticStrain)
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"""
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compute_stress(material::PerfectPlasticity,
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ε::SymmetricTensor{2,3},
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state_old::Union{Nothing,PlasticityState}=nothing,
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Δt::Float64=0.0)
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compute_stress(material::PerfectPlasticity, ε, state_old, Δt) -> (σ, 𝔻, state_new)
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Compute stress and consistent tangent using radial return mapping.
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# Algorithm
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1. Elastic predictor: σ_trial = 𝔻 : (ε - ε^p_old)
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2. Check yield: f = √(3/2)||dev(σ_trial - α)|| - σ_y
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3. Plastic corrector (if f > 0):
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- Compute flow direction: n = dev(σ_trial - α) / ||dev(σ_trial - α)||
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- Solve for plastic multiplier: Δλ = f / (3μ + H)
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- Update stress: σ = σ_trial - 2μΔλ·n
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- Update backstress: α_new = α + (2/3)HΔλ·n
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- Update plastic strain: ε^p_new = ε^p + Δλ·n
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4. Consistent tangent: 𝔻^ep = 𝔻 - (4μ²/(3μ+H))·(n⊗n)
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# Arguments
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- `material::PerfectPlasticity` - Material parameters
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- `ε::SymmetricTensor{2,3}` - Total strain tensor
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- `state_old::NamedTuple` - Previous state (empty = initial): (ε_p, α, κ)
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- `Δt::Float64` - Time increment (unused for rate-independent plasticity)
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# Returns
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- `σ::SymmetricTensor{2,3}` - Cauchy stress tensor
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- `𝔻::SymmetricTensor{4,3}` - Consistent tangent modulus
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- `state_new::NamedTuple` - Updated state: (ε_p, α, κ)
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# Performance
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~200-500 ns per evaluation (elastic), ~300-600 ns (plastic)
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"""
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function compute_stress(material::PerfectPlasticity,
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ε::SymmetricTensor{2,3},
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@@ -318,11 +168,6 @@ end
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symmetric_identity_tensor()
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Fourth-order symmetric identity tensor: 𝕀 = ½(δᵢₖδⱼₗ + δᵢₗδⱼₖ)
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Used in constructing elastic tangent: 𝔻 = λ·I⊗I + 2μ·𝕀
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# Returns
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`SymmetricTensor{4,3,Float64}` - Symmetric identity tensor
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"""
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@inline function symmetric_identity_tensor()
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# Construct 4th order identity with major and minor symmetry
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