Added tests for themal laws

src/PhysicalModels/ThermoMechanicalModels.jl

@@ -146,7 +146,7 @@ end
 function derivatives(law::LogisticLaw)
   @unpack θr, μ, σ = law
   z(x) = (log(x) - μ) / σ
-  std_pdf(x) = 1/σ/sqrt(2 * π) * exp(-z(x)^2 / 2)
+  std_pdf(x) = 1/(σ*sqrt(2 * π)) * exp(-z(x)^2 / 2)
   std_cdf(x) = 0.5 * (1 + erf(z(x) / sqrt(2)))
   ξR = 1 / (1-std_cdf(θr))
   f(θ) = ξR * (1-std_cdf(θ))

src/TensorAlgebra/Functions.jl

@@ -25,7 +25,7 @@ end
 """
 Fast and dependency-free implementation of erf function, up to 1e-6 precision.
 """
-@inline function erf(x::Float64)
+@inline function erf(x::Real)
   p  = 0.3275911
   a1 = 0.254829592
   a2 = -0.284496736

test/TestConstitutiveModels/ThermalLawsTests.jl

@@ -0,0 +1,12 @@
+using ForwardDiff
+using HyperFEM
+using Test
+
+@testset "LogisticLaw" begin
+  law = LogisticLaw(273.15, log(300.1), 0.11)
+  f, df, ddf = derivatives(law)
+  for θ ∈ 200.0:50:400  # NOTE: The numerical derivative of erf is a bad approximation, while the analyitical function uses the exact value.
+    @test isapprox(df(θ), ForwardDiff.derivative(f, θ), rtol=1e-3)
+    @test isapprox(ddf(θ), ForwardDiff.derivative(df, θ), rtol=1e-10)
+  end
+end

test/TestConstitutiveModels/runtests.jl

@@ -15,4 +15,8 @@ using Test
     include("ElectroMechanicalTests.jl")
   end
 
+  @time begin
+    include("ThermalLawsTests.jl")
+  end
+
 end