LinearElastic

struct LinearElasticity <: ConstitutiveModels.AbstractHyperelasticity

helmholtz_free_energy(
    model::LinearElasticity,
    props,
    ∇u::Tensors.Tensor{2, 3, T, 9},
    θ
) -> Any

initialize_props(
    _::LinearElasticity,
    inputs::Dict{String}
) -> Any

Simple shear

Analytic solution

Fill me out

Verification

Here is a comparison of an analytic solution to the uniaxial stress boundary value problem in displacement control.

using ConstitutiveModels
using Plots

function linearelastic_simple_shear()
    inputs = Dict(
        "density"         => 1.0,
        "Young's modulus" => 1.0,#u"MPa",
        "Poisson's ratio" => 0.3
    )

    model = LinearElastic()
    motion = SimpleShear(t -> 0.01t)
    out = simulate_material_point(cauchy_stress, model, inputs, motion, 1.0)
    props = initialize_props(model, inputs)
    εs = map(x -> x.kinematics, out)
    γs = map(x -> 2 * x[1, 2], εs)
    σs = map(x -> x.material_output, out)
    Zs = map(x -> x.state, out)

    μ = props[3]
    σ_11s_an = 0. * γs
    σ_22s_an = 0. * γs
    σ_12s_an = μ * γs

    plot(motion, εs, σs, Zs, σ_11s_an, σ_22s_an, σ_12s_an)
end
linearelastic_simple_shear()

Uniaxial Strain

Analytic solution

Fill me out

Verification

Here is a comparison of an analytic solution to the uniaxial stress boundary value problem in displacement control.

using ConstitutiveModels
using Plots

function linearelastic_uniaxial_strain()
    inputs = Dict(
        "density"         => 1.0,
        "Young's modulus" => 1.0,#u"MPa",
        "Poisson's ratio" => 0.3
    )
    model = LinearElastic()
    motion = UniaxialStrain(t -> 1 + 0.05t)
    out = simulate_material_point(cauchy_stress, model, inputs, motion, 1.0)
    props = initialize_props(model, inputs)
    εs = map(x -> x.kinematics, out)
    λs = map(x -> x[1, 1] + 1, εs)
    σs = map(x -> x.material_output, out)
    Zs = map(x -> x.state, out)

    λ, μ = props[2], props[3]
    σ_11s_an = λ * (λs .- 1.) .+ 2. * μ * (λs .- 1.)
    σ_22s_an = λ * (λs .- 1.)
    plot(motion, εs, σs, Zs, σ_11s_an, σ_22s_an)

end

linearelastic_uniaxial_strain()