# Example Applications¶

Ratel provides several examples for direct use as simulation drivers and as starters for more complete applications and workflows. See Using Ratel for common options to specify the mesh, materials, algebraic solvers, etc.

## Static Example¶

This code solves the steady-state static momentum balance equations using unstructured high-order finite/spectral element spatial discretizations. We consider linear and three different hyperelastic materials in solid mechanics applications:

Linear elasticity

Neo-Hookean hyperelasticity at finite strain

Mooney-Rivlin hyperelasticity at finite strain

Ogden hyperelasticity at finite strain

formulated for compressible and incompressible materials.

In the top level directory, build by using:

```
$ make examples
```

and run with:

```
$ ./build/ex01-static -options_file [.yml file] -view_diagnostic_quantities
```

## Quasistatic Example¶

This code solves the same steady-state formulation as the static solver example, but with an additional time stepping parameter for boundary conditions and forcing terms.

In the top level directory, build by using:

```
$ make examples
```

and run with:

```
$ ./build/ex02-quasistatic -options_file [.yml file] -view_diagnostic_quantities
```

The quasistatic formulation is built off of the PETSc Time Stepper (TS) object.

## Dynamic Solver¶

The dynamic solver example solves the momentum balance equations with the same constitutive models as the static and quasistatic examples.

In the top level directory, build by using:

```
$ make examples
```

and run with:

```
$ ./build/ex03-dynamic -options_file [.yml file] -view_diagnostic_quantities
```

The dynamic formulation uses the TSAlpha2 PETSc Time Stepper (TS) object, which implements the implicit Generalized-Alpha method for second-order systems.