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jmartfrut merged 1 commit into from
Jan 22, 2026
Merged

Adds the Gent2D constitutive model #106

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1 change: 1 addition & 0 deletions src/Exports.jl
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Expand Up @@ -25,6 +25,7 @@ end
@publish PhysicalModels LinearElasticity3D
@publish PhysicalModels LinearElasticity2D
@publish PhysicalModels Yeoh3D
@publish PhysicalModels Gent2D
@publish PhysicalModels NeoHookean3D
@publish PhysicalModels IncompressibleNeoHookean3D
@publish PhysicalModels IncompressibleNeoHookean2D
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84 changes: 62 additions & 22 deletions src/PhysicalModels/MechanicalModels.jl
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Expand Up @@ -144,12 +144,12 @@ Base.hcat(a::AnisoElastic...) = MultiAnisoElastic(a)


function (obj::MultiAnisoElastic)(args...)
DΨ = map(a -> a(args...), obj.Models)
Ψα = map(x -> x[1], DΨ)
∂Ψα∂F = map(x -> x[2], DΨ)
DΨ = map(a -> a(args...), obj.Models)
Ψα = map(x -> x[1], DΨ)
∂Ψα∂F = map(x -> x[2], DΨ)
∂Ψα∂FF = map(x -> x[3], DΨ)
Ψ(F, N) = mapreduce((Ψi, Ni) -> Ψi(F, Ni), +, Ψα, N)
∂Ψ∂F(F, N) = mapreduce((∂Ψi∂F, Ni) -> ∂Ψi∂F(F, Ni), +, ∂Ψα∂F, N)
Ψ(F, N) = mapreduce((Ψi, Ni) -> Ψi(F, Ni), +, Ψα, N)
∂Ψ∂F(F, N) = mapreduce((∂Ψi∂F, Ni) -> ∂Ψi∂F(F, Ni), +, ∂Ψα∂F, N)
∂Ψ∂FF(F, N) = mapreduce((∂Ψi∂FF, Ni) -> ∂Ψi∂FF(F, Ni), +, ∂Ψα∂FF, N)
(Ψ, ∂Ψ∂F, ∂Ψ∂FF)
end
Expand Down Expand Up @@ -280,6 +280,46 @@ struct NeoHookean3D <: IsoElastic
end


struct Gent2D <: IsoElastic
λ::Float64
μ::Float64
Jm::Float64
γ::Float64
ρ::Float64

function Gent2D(; λ::Float64, μ::Float64, Jm::Float64, γ::Float64, ρ::Float64=0.0)
new(λ, μ, Jm, γ, ρ)
end

function (obj::Gent2D)(Λ::Float64=1.0)
λ, μ, Jm, γ, ρ = obj.λ, obj.μ, obj.Jm, obj.γ, obj.ρ

J(F) = det(F)
H(F) = det(F) * inv(F)'
I1(F) = tr(F' * F) + 1.0

Ψiso(F) = -μ * Jm / 2.0 * log(1.0 - (I1(F) - 3.0) / Jm)
Ψvol(F) = -μ * log(J(F)) + λ * (J(F)^γ + J(F)^(-γ)) - 2.0 * λ
Ψ(F) = Ψiso(F) + Ψvol(F)

∂Ψ_∂F(F) = F * μ / (1.0 - (I1(F) - 3.0) / Jm)
∂Ψ_∂J(F) = -μ * (1.0 / J(F)) + λ * γ * (J(F)^(γ - 1.0) - J(F)^(-γ - 1.0))
∂Ψu(F) = ∂Ψ_∂F(F) + ∂Ψ_∂J(F) * H(F)

∂Ψ2_∂FF(F) = (μ / (1.0 - (I1(F) - 3.0) / Jm)) * I4 + 2.0 * (μ / (Jm * (1.0 - (I1(F) - 3.0) / Jm)^2)) * (F ⊗ F)
∂Ψ2_∂JJ(F) = μ * (1.0 / (J(F)^2)) +
λ * γ * ((γ - 1.0) * J(F)^(γ - 2.0) + (γ + 1.0) * J(F)^(-γ - 2.0))

∂Ψuu(F) = ∂Ψ2_∂FF(F) +
∂Ψ2_∂JJ(F) * (H(F) ⊗ H(F)) +
∂Ψ_∂J(F) * _∂H∂F_2D()

return (Ψ, ∂Ψu, ∂Ψuu)
end
end



struct MooneyRivlin3D <: IsoElastic
λ::Float64
μ1::Float64
Expand Down Expand Up @@ -326,7 +366,7 @@ struct MooneyRivlin2D <: IsoElastic
J(F) = det(F)
H(F) = det(F) * inv(F)'
Ψ(F) = (μ1 / 2 + μ2 / 2) * tr((F)' * F) + μ2 / 2.0 * J(F)^2 - (μ1 + 2 * μ2) * logreg(J(F)) +
(λ / 2.0) * (J(F) - 1)^2 -(μ1 + μ2) - μ2/2
(λ / 2.0) * (J(F) - 1)^2 - (μ1 + μ2) - μ2 / 2
∂Ψ_(F) = ForwardDiff.gradient(F -> Ψ(F), get_array(F))
∂2Ψ_(F) = ForwardDiff.jacobian(F -> ∂Ψ_(F), get_array(F))

Expand Down Expand Up @@ -355,7 +395,7 @@ struct NonlinearMooneyRivlin3D <: IsoElastic

Ψ(F) = μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * (tr((F)' * F))^α1 + μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * (tr((H(F))' * H(F)))^α2 - (μ1 + 2 * μ2) * logreg(J(F)) +
(λ / 2.0) * (J(F) - 1)^2 +
-μ1/(2.0 * α1 * 3.0^(α1 - 1))*3^α1 -μ2/(2.0 * α2 * 3.0^(α2 - 1))*3^α2
-μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 - μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * 3^α2

∂Ψ_∂F(F) = (μ1 / (3.0^(α1 - 1)) * (tr((F)' * F))^(α1 - 1)) * F
∂Ψ_∂H(F) = (μ2 / (3.0^(α2 - 1)) * (tr((H(F))' * H(F)))^(α2 - 1)) * H(F)
Expand Down Expand Up @@ -389,7 +429,7 @@ struct NonlinearMooneyRivlin2D <: IsoElastic
H(F) = det(F) * inv(F)'
Ψ(F) = μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * (tr((F)' * F) + 1.0)^α1 + μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * (tr((F)' * F) + J(F)^2)^α2 - (μ1 + 2.0 * μ2) * logreg(J(F)) +
(λ / 2.0) * (J(F) - 1)^2 +
-μ1/(2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 -μ2/(2.0 * α2 * 3.0^(α2 - 1)) * 3^α2
-μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 - μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * 3^α2

∂Ψ_∂F(F) = ((μ1 / (3.0^(α1 - 1)) * (tr((F)' * F) + 1.0)^(α1 - 1)) + μ2 / (3.0^(α2 - 1)) * (tr((F)' * F) + J(F)^2)^(α2 - 1)) * F
∂log∂J(J) = J >= Threshold ? 1 / J : (2 / Threshold - J / (Threshold^2))
Expand Down Expand Up @@ -427,7 +467,7 @@ struct NonlinearMooneyRivlin2D_CV <: IsoElastic
H(F) = det(F) * inv(F)'
Ψ(F) = μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * (tr((F)' * F) + 1.0)^α1 + μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * (tr((F)' * F) + J(F)^2)^α2 - (μ1 + 2.0 * μ2) * log(J(F)) +
λ * (J(F)^(γ) + J(F)^(-γ)) +
-μ1/(2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 -μ2/(2.0 * α2 * 3.0^(α2 - 1)) * 3^α2 -2λ
-μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 - μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * 3^α2 - 2λ

∂Ψ_∂F(F) = ((μ1 / (3.0^(α1 - 1)) * (tr((F)' * F) + 1.0)^(α1 - 1)) + μ2 / (3.0^(α2 - 1)) * (tr((F)' * F) + J(F)^2)^(α2 - 1)) * F
∂Ψ_∂J(F) = μ2 / (3.0^(α2 - 1)) * J(F) * (tr((F)' * F) + J(F)^2)^(α2 - 1) - (μ1 + 2.0 * μ2) * (1.0 / J(F)) + λ * γ * (J(F)^(γ - 1) - J(F)^(-γ - 1))
Expand Down Expand Up @@ -463,9 +503,9 @@ struct NonlinearMooneyRivlin_CV <: IsoElastic
Ψ(F) = μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * (tr((F)' * F))^α1 +
μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * (tr((H(F))' * H(F)))^α2 -
(μ1 + 2 * μ2) * log(J(F)) + λ * (J(F)^(γ) + J(F)^(-γ)) +
-μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 +
-μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * 3^α2 +
-2λ
-μ1 / (2.0 * α1 * 3.0^(α1 - 1)) * 3^α1 +
-μ2 / (2.0 * α2 * 3.0^(α2 - 1)) * 3^α2 +
-2λ

∂Ψ_∂F(F) = ((μ1 / (3.0^(α1 - 1)) * (trAA(F))^(α1 - 1))) * F
∂Ψ_∂H(F) = ((μ2 / (3.0^(α2 - 1)) * (tr((H(F))' * H(F)))^(α2 - 1))) * H(F)
Expand Down Expand Up @@ -499,7 +539,7 @@ struct NonlinearNeoHookean_CV <: IsoElastic
J(F) = det(F)
H(F) = det(F) * inv(F)'
Ψ(F) = μ / (2.0 * α * 3.0^(α - 1)) * (tr((F)' * F))^α - μ * log(J(F)) + λ * (J(F)^(γ) + J(F)^(-γ)) +
-μ / (2.0 * α * 3.0^(α - 1)) * 3.0^α - 2λ
-μ / (2.0 * α * 3.0^(α - 1)) * 3.0^α - 2λ

∂Ψ_∂F(F) = ((μ / (3.0^(α - 1)) * (tr((F)' * F))^(α - 1))) * F
∂Ψ_∂J(F) = -μ * (1.0 / J(F)) + λ * γ * (J(F)^(γ - 1) - J(F)^(-γ - 1))
Expand Down Expand Up @@ -537,8 +577,8 @@ struct NonlinearIncompressibleMooneyRivlin2D_CV <: IsoElastic
∂e2_∂J2(F) = (10 / 9) * J(F)^(-8 / 3) * (tr((F)' * F) + 1.0)
∂e2_∂FJ(F) = -(4 / 3) * J(F)^(-5 / 3) * F

Ψ1(F) = μ / (2 * α) * (e(F))^α -μ / (2α) * 3^α
Ψ2(F) = (λ) * (J(F)^(γ) + J(F)^(-γ)) -2λ
Ψ1(F) = μ / (2 * α) * (e(F))^α - μ / (2α) * 3^α
Ψ2(F) = (λ) * (J(F)^(γ) + J(F)^(-γ)) - 2λ
Ψ(F) = Ψ1(F) + Ψ2(F)

∂Ψ1_∂F(F) = (μ / 2) * (((e(F))^(α - 1.0)) * ∂e_∂F(F))
Expand Down Expand Up @@ -579,8 +619,8 @@ struct EightChain <: IsoElastic
C_iso = J(F)^(-2 / 3) * C
β = sqrt(tr(C_iso) / 3 / N)
L = β * (3.0 - β^2) / (1.0 - β^2)
L0 = (3N-1)/(N-1)/sqrt(N)
μ * N * (β * L + log(L / sinh(L)) - L0/sqrt(N) - log(L0 / sinh(L0)))
L0 = (3N - 1) / (N - 1) / sqrt(N)
μ * N * (β * L + log(L / sinh(L)) - L0 / sqrt(N) - log(L0 / sinh(L0)))
end

∂Ψ∂F(F) = begin
Expand Down Expand Up @@ -864,7 +904,7 @@ struct IncompressibleNeoHookean2D <: IsoElastic
J1 = 0.5 * (1.0 + sqrt(1.0 + δ^2))
∂J1 = 0.5 * (1.0 + 1.0 / sqrt(1.0^2 + δ^2))
β = μ * (J1^(-2 / 3) - J1^(-5 / 3) * ∂J1)
Ψ1(F) = μ / 2 * (tr((F)' * F) + 1.0) * J(F)^(-2 / 3) - 3μ/2 * J(I2)^(-2 / 3)
Ψ1(F) = μ / 2 * (tr((F)' * F) + 1.0) * J(F)^(-2 / 3) - 3μ / 2 * J(I2)^(-2 / 3)
Ψ2(F) = (λ / 2) * (J_(F) - 1)^2
Ψ(F) = Ψ1(F) + Ψ2(F) - β * log(J_(F))

Expand Down Expand Up @@ -898,8 +938,8 @@ struct IncompressibleNeoHookean2D_CV <: IsoElastic
λ, μ, γ = obj.λ, obj.μ, obj.γ
J(F) = det(F)
H(F) = det(F) * inv(F)'
Ψ1(F) = μ / 2 * (tr((F)' * F) + 1.0) * J(F)^(-2 / 3) -3μ/2
Ψ2(F) = λ * (J(F)^(γ) + J(F)^(-γ)) -2λ
Ψ1(F) = μ / 2 * (tr((F)' * F) + 1.0) * J(F)^(-2 / 3) - 3μ / 2
Ψ2(F) = λ * (J(F)^(γ) + J(F)^(-γ)) - 2λ
Ψ(F) = Ψ1(F) + Ψ2(F)

∂Ψ1_∂J(F) = -μ / 3 * (tr((F)' * F) + 1.0) * J(F)^(-5 / 3)
Expand Down Expand Up @@ -937,7 +977,7 @@ struct ARAP2D_regularized <: IsoElastic
J1 = 0.5 * (1.0 + sqrt(1.0 + δ^2))
∂J1 = 0.5 * (1.0 + 1.0 / sqrt(1.0^2 + δ^2))
β = μ * (J1^(-1) - J1^(-2) * ∂J1)
Ψ(F) = μ * 0.5 * J(F)^(-1) * (tr((F)' * F)) - β * log(J_(F)) -μ*J(I2)^-1
Ψ(F) = μ * 0.5 * J(F)^(-1) * (tr((F)' * F)) - β * log(J_(F)) - μ * J(I2)^-1

∂Ψ1_∂J(F) = -μ / 2 * (tr((F)' * F)) * J(F)^(-2)
∂Ψ2_∂J(F) = -β / J_(F)
Expand Down Expand Up @@ -969,7 +1009,7 @@ struct ARAP2D <: IsoElastic
μ = obj.μ
J(F) = det(F)
H(F) = det(F) * inv(F)'
Ψ(F) = μ * 0.5 * J(F)^(-1) * (tr((F)' * F)) -μ
Ψ(F) = μ * 0.5 * J(F)^(-1) * (tr((F)' * F)) - μ
∂Ψ_∂F(F) = μ * F * J(F)^(-1)
∂Ψ_∂J(F) = -μ / 2 * (tr((F)' * F)) * J(F)^(-2)

Expand Down
1 change: 1 addition & 0 deletions src/PhysicalModels/PhysicalModels.jl
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Expand Up @@ -16,6 +16,7 @@ import Base: +
import Gridap: update_state!

export Yeoh3D
export Gent2D
export NeoHookean3D
export IncompressibleNeoHookean3D
export IncompressibleNeoHookean2D
Expand Down
7 changes: 7 additions & 0 deletions test/TestConstitutiveModels/PhysicalModelTests.jl
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Expand Up @@ -246,6 +246,13 @@ end
test_equilibrium_at_rest_3D(model)
end

@testset "Gent2D" begin
# Memory estimate: 0 bytes, allocs estimate: 0.
model = Gent2D(λ=3.0, μ=1.0, Jm=1000.0, γ=1.0)
test_derivatives_2D_(model, Kinematics(Mechano, Solid))
test_equilibrium_at_rest_2D(model)
end


@testset "MooneyRivlin2D" begin
# Memory estimate: 0 bytes, allocs estimate: 0.
Expand Down