Added SaintVenant

docs/src/finite_strains.md

@@ -12,6 +12,10 @@ the `MaterialModelsBase.jl` interface.
 NeoHooke
 CompressibleNeoHooke
 ```
+### Saint-Venant Elasticity
+```@docs 
+SaintVenant
+```
 
 ## [Plasticity](@id finite_strain_plasticity)
 ```@docs

src/MechanicalMaterialModels.jl

@@ -51,7 +51,8 @@ export CrystalPlasticity
 
 include("hyper_elasticity/HyperElastic.jl")
 include("hyper_elasticity/NeoHooke.jl")
-export NeoHooke, CompressibleNeoHooke
+include("hyper_elasticity/SaintVenant.jl")
+export NeoHooke, CompressibleNeoHooke, SaintVenant
 
 include("FiniteStrainPlastic.jl")
 export FiniteStrainPlastic

src/hyper_elasticity/SaintVenant.jl

@@ -0,0 +1,20 @@
+
+"""
+    SaintVenant(; elastic)
+
+The Saint-Venant formulation defined by the potential
+```math
+\\varPsi(\\boldsymbol{E}) = \\frac{1}{2}\\boldsymbol{E}:\\boldsymbol{C}:\\boldsymbol{E}
+```
+where ``\\boldsymbol{E}`` is the Green-Lagrange strain tensor and ``\\boldsymbol{C}`` is the elastic stiffness tensor.
+"""
+@kwdef struct SaintVenant{E} <: AbstractHyperElastic
+    elastic::E
+end
+
+function compute_potential(m::SaintVenant, C::SymmetricTensor)
+    E = 0.5 * (C - one(C))
+    return 1/2 * E ⊡ m.elastic.C ⊡ E
+end
+
+MMB.get_vector_eltype(::SaintVenant{T}) where {T} = T

test/test_hyperelastic.jl

@@ -1,5 +1,5 @@
 @testset "HyperElastic" begin
-    models = (NeoHooke(;G=rand()), CompressibleNeoHooke(;G=rand(), K=rand()))
+    models = (NeoHooke(;G=rand()), CompressibleNeoHooke(;G=rand(), K=rand()), SaintVenant(LinearElastic(E=rand(), ν=rand())))
     F = rand(Tensor{2,3})
     for model in models
         state = initial_material_state(model)