Linearization

The governing dynamical equations of field-matter interaction in thermoelastic materials as outlined in the previous chapters are highly nonlinear. Generally, it is hardly possible to find exact solutions even if the most simple problems that are still of some physical relevance are attacked. As stated in Chap. 5 already, one of the major disadvantages, namely that the equations are given in the spatial description, while boundary conditions for a solid body are usually prescribed in the reference configuration, has been removed by the introduction of a consistent material description for both the field equations and the jump and boundary conditions. Nevertheless, the resulting equations are still highly nonlinear, and this implies that some approximation scheme must be found.