abstract type AbstractElementFormulation{ND, NF}

struct PlaneStrain <: AbstractMechanicsElementFormulation{2}

struct ThreeDimensional <: AbstractMechanicsElementFormulation{3}

discrete_gradient(_::PlaneStrain, ∇N_X) -> Any

discrete_gradient(_::ThreeDimensional, ∇N_X) -> Any

discrete_symmetric_gradient(_::PlaneStrain, ∇N_X) -> Any

discrete_symmetric_gradient(
    _::ThreeDimensional,
    ∇N_X
) -> Any

discrete_values(_::PlaneStrain, N) -> Any

discrete_values(_::ThreeDimensional, N) -> Any

extract_stiffness(
    _::PlaneStrain,
    A::Tensors.Tensor{4, 3, T<:Number, 81}
) -> StaticArraysCore.SArray

extract_stiffness(
    _::ThreeDimensional,
    A_in::Tensors.Tensor{4, 3, T<:Number, 81}
) -> StaticArraysCore.SArray

extract_stress(
    _::PlaneStrain,
    P::Tensors.Tensor{2, 3, T<:Number, 9}
) -> StaticArraysCore.SArray

extract_stress(
    _::ThreeDimensional,
    P::Tensors.Tensor{2, 3, T<:Number, 9}
) -> StaticArraysCore.SArray

modify_field_gradients(
    _::PlaneStrain,
    ∇u_q::StaticArraysCore.SArray{Tuple{2, 2}, T<:Number, 2, 4}
) -> Tensors.Tensor{2, 3, _A, 9} where _A

modify_field_gradients(
    _::ThreeDimensional,
    ∇u_q::StaticArraysCore.SArray{Tuple{3, 3}, T<:Number, 2, 9}
) -> Tensors.Tensor{2, 3, T, 9} where T<:Number

num_dimensions(_::AbstractElementFormulation{ND, NF}) -> Any

scatter_with_gradients!(
    storage::FiniteElementContainers.AbstractField,
    form::AbstractElementFormulation{ND, NF},
    e,
    conns,
    ∇N_X,
    vals
)

Method to in place take a set of vals and calculate fi = G * vals where is the discretegradient

scatter_with_gradients_and_gradients!(
    storage::AbstractVector,
    _::AbstractElementFormulation{ND, NF},
    e,
    conns,
    ∇N_X,
    k::Number
)

scalar case to calculate in place things like Kel = k∇NX ⋅ ∇N_X'

Case for total lagrange formulations of solid mechanics or other physics that need fourth order full 81 component tensors in 3d

Scalar equation specialization f_el = N * vals

General vector specialization f_el = N * vals

scalar implementation