(examples)= # Example Applications Ratel provides several examples for direct use as simulation drivers and as starters for more complete applications and workflows. See {ref}`using` for common options to specify the mesh, materials, algebraic solvers, etc. (example-static)= ## 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: ```console \$ make examples ``` and run with: ```console \$ ./build/ex01-static -options_file [.yml file] -view_diagnostic_quantities ``` (example-quasistatic)= ## 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: ```console \$ make examples ``` and run with: ```console \$ ./build/ex02-quasistatic -options_file [.yml file] -view_diagnostic_quantities ``` The quasistatic formulation is built off of the [PETSc Time Stepper (TS) object](https://petsc.org/release/docs/manualpages/TS/index.html). (example-dynamic)= ## 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: ```console \$ make examples ``` and run with: ```console \$ ./build/ex03-dynamic -options_file [.yml file] -view_diagnostic_quantities ``` The dynamic formulation uses the TSAlpha2 [PETSc Time Stepper (TS) object](https://petsc.org/release/docs/manualpages/TS/index.html), which implements the implicit Generalized-Alpha method for second-order systems.