Solver Details

Since deal.II is a library and you are free to implement your own stuff, this section provides details about the implemented solver analogous to the commented tutorial programs in deal.II. In case you want to modify this solver or use it for your own project, the mathematical aspects should help you start. In case you want to know more about capability of the implemented model, have a look in the section below.

Mathematical Aspects

This program was built on the step-8 tutorial program of the deal.II library, which deals with linear elastostatics. A lot of aspects are already explained there. However, this program deals with linear elastodynamics. Therefore, we need to consider inertial effects. Our starting equation read as follows:

Where u is the displacement field, rho the material density, b the body forces and sigma the stress tensor, which is related to the linear strain measure epsilon via the fourth order elasticity tensor C. Equation (1.1) needs to be satisfied in the whole domain Omega and we apply the following boundary conditions:

Here, the first boundary condition is applied to the Dirichlet boundary Gamma_u and we prescribe a zero displacement. The second boundary condition is applied to the Neumann boundary Gamma_sigma and describes basically our coupling interface, since the traction vector is obtained from our flow solver. As last point, the initial condition are given in in equation 1.3:

Both initial values are chosen to be zero, but you are free to choose them differently according to your problem.

Discretization

Capability