## Snippet: An Abaqus inp example

An example to show the inp file structure. The example demonstrates the stretch of a square plate with the dimension $1 \times 1 \mathrm{m^2}$. The plate material is steel with elastic stiffness of $2.1 \times 10^{11} \mathrm{MPa}$. The material density is $7800 \mathrm{kg/m^3}$. The left boundary is fixed and $0.1 \mathrm{m}$ displacement is applied to the right boundary. The plane strain is assumed in the model. Here are the model and the simulation results.

## Snippet: Plot format in Wolfram

This snippet demonstrates the polt format that I often used in Wolfram Mathematica.

Plot[Sin[x], {x, -Pi, Pi},
Mesh->None, PlotRange->{{-Pi, Pi}, {-2, 2}},
AspectRatio->9/16, PlotTheme->"Scientific", FrameStyle->Black,
TicksStyle->Directive[FontSize->20], ImageSize->Large,
AxesLabel->Automatic, LabelStyle->Directive[FontSize->20,
FontFamily->"Times New Roman"], Epilog->{Text[Style[
ToExpression[ "y = 12 \\frac{\\partial^2 f(x)}{\\partial x^2}",
TeXForm, HoldForm], FontFamily->"Times New Roman", FontSize->20,
Bold, Black], Scaled[{.25, .80}]]}]

Here is the diagram,

Here is the Wolfram notebook (Ua98n5.nb) used in this post.

## Snippet: Matrix with Euler angles

This snippet posts an Excel to calculate the matrix with Euler angles. To describe the rotation of a crystal frame, commonly, we use three angles: $\alpha$, $\beta$, and $\gamma$. They are also known as Bunge angles.

The matrix to rotate the crystal frame in reference frame is described by Euler angles as below:

$$\displaystyle \mathbf{B}=\begin{bmatrix} \begin{matrix} \cos(\alpha)\cos(\gamma) \\ – \sin(\alpha)\sin(\gamma)\cos(\beta) \end{matrix}& \begin{matrix} \sin(\alpha)\cos(\gamma) \\ +\cos(\alpha)\sin(\gamma)\cos(\beta) \end{matrix}& \sin(\gamma)\sin(\beta)\\ \begin{matrix} -\cos(\alpha)\sin(\gamma) \\ – \sin(\alpha)\cos(\gamma)\cos(\beta) \end{matrix}& \begin{matrix} -\sin(\alpha)\sin(\gamma) \\ + \cos(\alpha)\cos(\gamma)\cos(\beta) \end{matrix}& \cos(\gamma)\sin(\beta)\\ \sin(\alpha)\sin(\beta) & -\cos(\alpha)\sin(\beta) & \cos(\beta) \end{bmatrix}$$

In this Excel (Cf06b0.xlsx), you just need to input three Euler angles and the vector in reference frame. It will give the matrix and the inverse matrix with these three Euler angles. Also, it will give the vector in crystal frame.

This snippet is very useful for debugging the code with the rotation of Euler angles.