Added SaintVenant (#10)

Author: GunnarssonJ

docs/src/finite_strains.md

@@ -6,6 +6,11 @@ Implementations of mechanical (stress-strain) material models following
 the `MaterialModelsBase.jl` interface. 
 
 
+### Saint-Venant Elasticity
+```@docs 
+SaintVenant
+```
+
 ## Hyperelasticity
 ### Neo-Hookean Materials
 ```@docs 

src/Elastic.jl

@@ -20,20 +20,20 @@ LinearElastic(::Val{:isotropic})
     LinearElastic{:general}(C::SymmetricTensor{4,3})
 
 Create a general `LinearElastic` material with the 4th order elastic stiffness tensor
-``\\boldsymbol{C}``, such that 
-``\\boldsymbol{\\sigma} = \\boldsymbol{C}:\\boldsymbol{\\epsilon}``. 
+``\\mathsf{\\boldsymbol{C}}``, such that 
+``\\boldsymbol{\\sigma} = \\mathsf{\\boldsymbol{C}}:\\boldsymbol{\\epsilon}``. 
 """
 LinearElastic(::Val{:general})
 
 """
     LinearElastic{:cubicsymmetry}(; C1111::T, C1122::T, C1212::T) where {T}
 
 Create a `LinearElastic` material where the stiffness tensor,
-``\\boldsymbol{C}``, possesses cubic symmetry along the coordinate axes.
-Using the 9-component Voigt notation, ``\\boldsymbol{C}`` can be expressed as
+``\\mathsf{\\boldsymbol{C}}``, possesses cubic symmetry along the coordinate axes.
+Using the 9-component Voigt notation, ``\\mathsf{\\boldsymbol{C}}`` can be expressed as
 
 ```math
-\\boldsymbol{C} = 
+\\mathsf{\\boldsymbol{C}} = 
 \\begin{bmatrix}
 C_{1111} & C_{1122} & C_{1122} & 0 & 0 & 0 & 0 & 0 & 0 \\\\
 C_{1122} & C_{1111} & C_{1122} & 0 & 0 & 0 & 0 & 0 & 0 \\\\

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 +1,21 @@
+
+"""
+    SaintVenant(elastic::LinearElastic)
+
+The Saint-Venant formulation defined by the potential
+```math
+\\varPsi(\\boldsymbol{E}) = \\frac{1}{2}\\boldsymbol{E}:\\mathsf{\\boldsymbol{C}}:\\boldsymbol{E}
+```
+where ``\\boldsymbol{E}`` is the Green-Lagrange strain tensor and ``\\mathsf{\\boldsymbol{C}}`` is the 
+elastic stiffness tensor defined in `elastic`.
+"""
+struct SaintVenant{E} <: AbstractHyperElastic
+    elastic::E
+end
+
+function compute_potential(m::SaintVenant, C::SymmetricTensor)
+    E = (C - one(C)) / 2
+    return (E ⊡ m.elastic.C ⊡ E) / 2
+end
+
+MMB.get_vector_eltype(m::SaintVenant) = MMB.get_vector_eltype(m.elastic)

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()/2)))
     F = rand(Tensor{2,3})
     for model in models
         state = initial_material_state(model)