feat(materials): add Mooney–Rivlin, Yeoh, and Gent hyperelastic laws

Provide additional `StatelessStrainDependent` models alongside Neo-Hookean.

- Implement strain-energy densities and `compute_stress` bridges for common hyperelastic forms.

src/materials/hyperelastic_models.jl

@@ -0,0 +1,172 @@
+# SPDX-FileCopyrightText: 2015-2026 Jukka Aho
+# SPDX-License-Identifier: MIT
+
+"""
+Additional compressible hyperelastic potentials using Green–Lagrange strain `E`
+through `C = 2E + I` and automatic differentiation (`Tensors.hessian`), matching
+[`NeoHookean`](@ref).
+
+Models: [`MooneyRivlin`](@ref), [`Yeoh3`](@ref), [`Gent`](@ref).
+"""
+
+using Tensors
+
+@inline function _hyperelastic_J(C::SymmetricTensor{2,3})
+    d = det(C)
+    d > 0 || throw(DomainError(d, "det(C) must be positive"))
+    return √d
+end
+
+@inline function _second_invariant_C(C::SymmetricTensor{2,3})
+    trC = tr(C)
+    trCC = tr(C ⋅ C)
+    return 0.5 * (trC * trC - trCC)
+end
+
+function _hyperelastic_stress_tangent(ψ, C::SymmetricTensor{2,3})
+    ∂²ψ∂C², ∂ψ∂C = Tensors.hessian(ψ, C, :all)
+    S = 2 * ∂ψ∂C
+    𝔻 = 4 * ∂²ψ∂C²
+    return S, 𝔻
+end
+
+function _compute_from_E(material, E::SymmetricTensor{2,3,T}) where T
+    I = one(E)
+    C = 2E + I
+    ψ(C_) = strain_energy(material, C_)
+    S, 𝔻 = _hyperelastic_stress_tangent(ψ, C)
+    return S, 𝔻, NamedTuple()
+end
+
+"""
+    MooneyRivlin <: AbstractElasticMaterial
+
+Compressible Mooney–Rivlin strain energy:
+
+`ψ = C₁₀ (I₁ − 3) + C₀₁ (I₂ − 3) + (κ/2)(J − 1)²`
+
+with `I₁ = tr(C)`, `I₂` the standard second invariant, `J = √det(C)`.
+"""
+struct MooneyRivlin <: AbstractElasticMaterial
+    C10::Float64
+    C01::Float64
+    κ_bulk::Float64
+
+    function MooneyRivlin(C10::Float64, C01::Float64, κ_bulk::Float64)
+        κ_bulk > 0 || throw(ArgumentError("bulk modulus κ_bulk must be positive"))
+        new(C10, C01, κ_bulk)
+    end
+end
+
+MooneyRivlin(; C10::Real, C01::Real, κ_bulk::Real) =
+    MooneyRivlin(Float64(C10), Float64(C01), Float64(κ_bulk))
+
+material_behavior(::MooneyRivlin) = StatelessStrainDependent()
+supported_physics(::MooneyRivlin) = (Elasticity{3}(),)
+required_state_variables(::MooneyRivlin) = ()
+
+function strain_energy(m::MooneyRivlin, C::SymmetricTensor{2,3})
+    J = _hyperelastic_J(C)
+    I1 = tr(C)
+    I2 = _second_invariant_C(C)
+    return m.C10 * (I1 - 3) + m.C01 * (I2 - 3) + (m.κ_bulk / 2) * (J - 1)^2
+end
+
+function compute_stress(m::MooneyRivlin, E::SymmetricTensor{2,3,T}, ::Nothing, Δt::Float64) where {T}
+    return _compute_from_E(m, E)
+end
+
+function compute_stress(m::MooneyRivlin, E::SymmetricTensor{2,3,T}, ::NamedTuple, Δt::Float64) where {T}
+    return _compute_from_E(m, E)
+end
+
+compute_stress(m::MooneyRivlin, E::SymmetricTensor{2,3}) = compute_stress(m, E, nothing, 0.0)
+
+"""
+    Yeoh3 <: AbstractElasticMaterial
+
+Three-term Yeoh expansion in `I₁`:
+
+`ψ = Σᵢ Cᵢ₀ (I₁ − 3)ⁱ` for `i ∈ {1,2,3}`, plus `(κ/2)(J − 1)²`.
+"""
+struct Yeoh3 <: AbstractElasticMaterial
+    C10::Float64
+    C20::Float64
+    C30::Float64
+    κ_bulk::Float64
+
+    function Yeoh3(C10::Float64, C20::Float64, C30::Float64, κ_bulk::Float64)
+        κ_bulk > 0 || throw(ArgumentError("bulk modulus κ_bulk must be positive"))
+        new(C10, C20, C30, κ_bulk)
+    end
+end
+
+Yeoh3(; C10::Real, C20::Real = 0.0, C30::Real = 0.0, κ_bulk::Real) =
+    Yeoh3(Float64(C10), Float64(C20), Float64(C30), Float64(κ_bulk))
+
+material_behavior(::Yeoh3) = StatelessStrainDependent()
+supported_physics(::Yeoh3) = (Elasticity{3}(),)
+required_state_variables(::Yeoh3) = ()
+
+function strain_energy(m::Yeoh3, C::SymmetricTensor{2,3})
+    J = _hyperelastic_J(C)
+    I1 = tr(C)
+    x = I1 - 3
+    return m.C10 * x + m.C20 * x^2 + m.C30 * x^3 + (m.κ_bulk / 2) * (J - 1)^2
+end
+
+function compute_stress(m::Yeoh3, E::SymmetricTensor{2,3,T}, ::Nothing, Δt::Float64) where {T}
+    return _compute_from_E(m, E)
+end
+
+function compute_stress(m::Yeoh3, E::SymmetricTensor{2,3,T}, ::NamedTuple, Δt::Float64) where {T}
+    return _compute_from_E(m, E)
+end
+
+compute_stress(m::Yeoh3, E::SymmetricTensor{2,3}) = compute_stress(m, E, nothing, 0.0)
+
+"""
+    Gent <: AbstractElasticMaterial
+
+Gent shear resistance with compressible volumetric penalty:
+
+`ψ = −(μ J_m / 2) log(1 − (I₁ − 3)/J_m) + (κ/2)(J − 1)²`
+
+Requires `I₁ − 3 < J_m`.
+"""
+struct Gent <: AbstractElasticMaterial
+    μ::Float64
+    Jm::Float64
+    κ_bulk::Float64
+
+    function Gent(μ::Float64, Jm::Float64, κ_bulk::Float64)
+        μ > 0 || throw(ArgumentError("μ must be positive"))
+        Jm > 0 || throw(ArgumentError("Jm must be positive"))
+        κ_bulk > 0 || throw(ArgumentError("bulk modulus κ_bulk must be positive"))
+        new(μ, Jm, κ_bulk)
+    end
+end
+
+Gent(; μ::Real, Jm::Real, κ_bulk::Real) = Gent(Float64(μ), Float64(Jm), Float64(κ_bulk))
+
+material_behavior(::Gent) = StatelessStrainDependent()
+supported_physics(::Gent) = (Elasticity{3}(),)
+required_state_variables(::Gent) = ()
+
+function strain_energy(m::Gent, C::SymmetricTensor{2,3})
+    J = _hyperelastic_J(C)
+    I1 = tr(C)
+    x = I1 - 3
+    x < m.Jm || throw(DomainError(x, "I₁ − 3 must be < Jm for Gent model"))
+    return -m.μ * m.Jm / 2 * log(1 - x / m.Jm) + (m.κ_bulk / 2) * (J - 1)^2
+end
+
+function compute_stress(m::Gent, E::SymmetricTensor{2,3,T}, ::Nothing, Δt::Float64) where {T}
+    return _compute_from_E(m, E)
+end
+
+function compute_stress(m::Gent, E::SymmetricTensor{2,3,T}, ::NamedTuple, Δt::Float64) where {T}
+    return _compute_from_E(m, E)
+end
+
+compute_stress(m::Gent, E::SymmetricTensor{2,3}) = compute_stress(m, E, nothing, 0.0)