Add tests for rotate_axes

src/transform.jl

@@ -29,14 +29,14 @@ for S in (:StiffnessTensor, :ComplianceTensor)
     @eval function rotate_axes(T::$S, Q::AbstractMatrix)
         @assert isrotation(Q)
         @einsum T′[i, j, k, l] := T[m, n, o, p] * Q[i, m] * Q[j, n] * Q[k, o] * Q[l, p]
-        return $S(T)
+        return $S(T′)
     end
 end
 for S in (:TensorStrain, :TensorStress)
     @eval function rotate_axes(T::$S, Q::AbstractMatrix)
         @assert isrotation(Q)
         @einsum T′[i, j] := T[k, l] * Q[i, k] * Q[j, l]
-        return $S(T)
+        return $S(T′)
     end
 end
 for S in (:StiffnessMatrix, :ComplianceMatrix, :EngineeringStrain, :EngineeringStress)

test/runtests.jl

@@ -6,4 +6,5 @@ using Test
     include("operations.jl")
     include("invariants.jl")
     include("axial.jl")
+    include("transform.jl")
 end

test/transform.jl

@@ -0,0 +1,110 @@
+using LinearAlgebra: diag
+
+@testset "Test example from notes (3.35)" begin
+    # TODO: See https://github.com/ahwillia/Einsum.jl/issues/43
+    for τ in (250,)
+        𝟘 = zero(τ)
+        σ = TensorStress([
+            𝟘 τ 𝟘
+            τ 𝟘 𝟘
+            𝟘 𝟘 𝟘
+        ])
+        Q = [
+            1 1 0
+            -1 1 0
+            0 0 √2
+        ] / √2
+        @test rotate_axes(σ, Q) ≈ TensorStress([
+            τ 𝟘 𝟘
+            𝟘 -τ 𝟘
+            𝟘 𝟘 𝟘
+        ])
+        @test rotate_axes(EngineeringStress(σ), Q) ≈ EngineeringStress(τ, -τ, 0, 0, 0, 0)
+    end
+end
+
+@testset "Test homework 3 question 1" begin
+    σ = TensorStress([
+        0 0 0
+        0 245 0
+        0 0 0
+    ])
+    Q = [
+        1 1 0
+        -1 1 0
+        0 0 √2
+    ] / √2
+    @test rotate_axes(σ, Q)[1, 2] ≈ sin(2 * pi / 4) / 2 * σ[2, 2]
+end
+
+@testset "Test homework 3 question 2" begin
+    σ = TensorStress([
+        300 100 0
+        100 100 0
+        0 0 0
+    ])
+    Q = θ -> [
+        cos(θ) sin(θ) 0
+        -sin(θ) cos(θ) 0
+        0 0 1
+    ]
+    @testset "Determine the principal stresses" begin
+        @test rotate_axes(σ, Q(pi / 8)) ≈ TensorStress([
+            200+100 * √2 0 0
+            0 200-100 * √2 0
+            0 0 0
+        ])
+    end
+    @testset "Determine the maximum in-plane shear" begin
+        @test rotate_axes(σ, Q(-pi / 8))[1, 2] == 100 * √2
+        @test rotate_axes(σ, Q(3pi / 8))[1, 2] == -100 * √2
+    end
+end
+
+@testset "Test question 5 in midterm 1, 2019" begin
+    σ₀ = 250
+    σ = TensorStress([
+        σ₀ 0 0
+        0 2σ₀ 0
+        0 0 0
+    ])
+    Q = [
+        1/√2 -1/√2 0
+        1/√6 1/√6 -2/√6
+        1/√3 1/√3 1/√3
+    ]
+    @test rotate_axes(σ, Q)[3, 1] ≈ -σ₀ / √6
+end
+
+@testset "Test question 6 in midterm 1, 2019" begin
+    σ₀ = 360
+    σ = TensorStress([
+        σ₀ σ₀/3 0
+        σ₀/3 σ₀ 0
+        0 0 0
+    ])
+    Q = θ -> [
+        cos(θ) sin(θ) 0
+        -sin(θ) cos(θ) 0
+        0 0 1
+    ]
+    @test rotate_axes(σ, Q(-pi / 4)) ≈ TensorStress(diagm([2σ₀ / 3, 4σ₀ / 3, 0]))
+    @test rotate_axes(σ, Q(pi / 4)) == TensorStress(diagm([4σ₀ / 3, 2σ₀ / 3, 0]))
+    @test principal_values(σ) ≈ [0, 2σ₀ / 3, 4σ₀ / 3]
+end
+
+@testset "Test using principal axes as rotation matrix" begin
+    ε = TensorStrain([
+        0.5 0.3 0.2
+        0.3 -0.2 -0.1
+        0.2 -0.1 0.1
+    ])
+    evecs = principal_axes(ε)'
+    normal_strains = rotate_axes(ε, evecs)
+    @test norm(normal_strains - [
+        -0.370577 0 0
+        0 0.115308 0
+        0 0 0.655269
+    ]) < 1e-6
+    @test principal_values(ε) ≈ diag(normal_strains)
+end