Constructors

Identity tensors

Second order tensor

julia> one(SecondOrderTensor{3})
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> one(SymmetricSecondOrderTensor{3})
3×3 SymmetricSecondOrderTensor{3, Float64, 6}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> one(Mat{2,2})
2×2 Tensor{Tuple{2, 2}, Float64, 2, 4}:
 1.0  0.0
 0.0  1.0

Fourth order tensor

julia> one(FourthOrderTensor{3})
3×3×3×3 FourthOrderTensor{3, Float64, 81}:
[:, :, 1, 1] =
 1.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

[:, :, 2, 1] =
 0.0  0.0  0.0
 1.0  0.0  0.0
 0.0  0.0  0.0

[:, :, 3, 1] =
 0.0  0.0  0.0
 0.0  0.0  0.0
 1.0  0.0  0.0

[:, :, 1, 2] =
 0.0  1.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

[:, :, 2, 2] =
 0.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  0.0

[:, :, 3, 2] =
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  1.0  0.0

[:, :, 1, 3] =
 0.0  0.0  1.0
 0.0  0.0  0.0
 0.0  0.0  0.0

[:, :, 2, 3] =
 0.0  0.0  0.0
 0.0  0.0  1.0
 0.0  0.0  0.0

[:, :, 3, 3] =
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  1.0

julia> one(SymmetricFourthOrderTensor{3})
3×3×3×3 SymmetricFourthOrderTensor{3, Float64, 36}:
[:, :, 1, 1] =
 1.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

[:, :, 2, 1] =
 0.0  0.5  0.0
 0.5  0.0  0.0
 0.0  0.0  0.0

[:, :, 3, 1] =
 0.0  0.0  0.5
 0.0  0.0  0.0
 0.5  0.0  0.0

[:, :, 1, 2] =
 0.0  0.5  0.0
 0.5  0.0  0.0
 0.0  0.0  0.0

[:, :, 2, 2] =
 0.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  0.0

[:, :, 3, 2] =
 0.0  0.0  0.0
 0.0  0.0  0.5
 0.0  0.5  0.0

[:, :, 1, 3] =
 0.0  0.0  0.5
 0.0  0.0  0.0
 0.5  0.0  0.0

[:, :, 2, 3] =
 0.0  0.0  0.0
 0.0  0.0  0.5
 0.0  0.5  0.0

[:, :, 3, 3] =
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  1.0

Other special tensors

Levi-Civita

Tensorial.levicivita — Function

levicivita(::Val{N} = Val(3))

Return N dimensional Levi-Civita tensor.

Examples

julia> ϵ = levicivita()
3×3×3 Tensor{Tuple{3, 3, 3}, Int64, 3, 27}:
[:, :, 1] =
 0   0  0
 0   0  1
 0  -1  0

[:, :, 2] =
 0  0  -1
 0  0   0
 1  0   0

[:, :, 3] =
  0  1  0
 -1  0  0
  0  0  0

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