diff --git a/web/content/docs/benchmarks/creepbgra/CreepBRGa.pandoc b/web/content/docs/benchmarks/creepbgra/CreepBRGa.pandoc index 76bd21ac23c81bec8570649874c7470c4be02512..01248a63f080c18ccecb7d2f8a616588149988a7 100644 --- a/web/content/docs/benchmarks/creepbgra/CreepBRGa.pandoc +++ b/web/content/docs/benchmarks/creepbgra/CreepBRGa.pandoc @@ -84,7 +84,7 @@ $\lambda$ the Lamé constant, $G$ the shear modulus, and $\otimes$ the tensor product notation. is a fourth order tensor. Substituting equation and the expression of $C$ -into the stress rate expression, equation , we have +into the stress rate expression, equation, we have $$\begin{gathered} \dot { \mathbf \sigma}= \mathbf{C} (\dot { \mathbf \epsilon}- \dot { \mathbf \epsilon}^T)- 2bG {\left\Vert{\mathbf s}\right\Vert}^{m-1} {\mathbf s} @@ -183,3 +183,49 @@ $$\begin{gathered} obtained by the present multidimensional scheme with the analytical solution is shown in the following figure: {{< img src="../bgra0.png" >}} + + +Python code +----------- +A short python snippet, to compute the values. +<details> +<summary> +Insert this into Paraview's ProgrammableFilter: +</summary> +```python +A = self.GetInputDataObject(0, 0) +numPoints = A.GetNumberOfPoints() +outSxx = vtk.vtkDoubleArray() +outSxx.SetName('analytic_strain_xx') +outSyy = vtk.vtkDoubleArray() +outSyy.SetName('analytic_strain_yy') +outSzz = vtk.vtkDoubleArray() +outSzz.SetName('analytic_strain_zz') +outSxy = vtk.vtkDoubleArray() +outSxy.SetName('analytic_strain_xy') +sigma0=5.0 +A=0.18 +m=5 +Q=54000 +E=25000 +R=8.314472 +sf=1. +t=100 +e0=-sigma0/E +c=-A*exp(-Q/(R*373.15))*pow(sigma0,m) +strain_zz=e0+c*t +nv=0.27 +G=0.5*E/(1+nv) +strain_rr=strain_zz + 0.5*sigma0/G+1.5*A*exp(-Q/(R*373.15))*pow(sigma0, m)*t +for i in range(0, numPoints): + outSxx.InsertNextValue(strain_rr) + outSyy.InsertNextValue(strain_zz) + outSzz.InsertNextValue(strain_rr) + outSxy.InsertNextValue(0) +output = self.GetOutput() +output.GetPointData().AddArray(outSxx) +output.GetPointData().AddArray(outSyy) +output.GetPointData().AddArray(outSzz) +output.GetPointData().AddArray(outSxy) +``` +</details>