Then the dissipation term evolves from the thermodynamic potential in a very natural way as well as the evolution equations for the internal variables emanate from the dissipation potential. An Eulerian setting is used. The coupled consistent tangent moduli are carefully derived. Numerical results of the thermally triggered necking of a circular bar and of the impact of a copper rod on a rigid wall are given. The displacement and traction interpolation functions are linear in time and quadratic in space.
All integrations are analytical, and are expressed in terms of twelve basic recurring integrals.
Causality is ensured by integrating only over the dynamically active parts of each element, and the algorithm presented is time-marching and implicit. The use of analytical integrations allows both unbounded and bounded domain problems to be solved without having to introduce special enclosing elements. All of these improved features allow for a formulation that is very efficient and accurate. The stability and accuracy of the elastodynamic boundary element algorithm is demonstrated by solving several example problems and comparing the results with available analytical and numerical solutions. The tangent maps associated to the finite rotation vector are used to compute the tangent matrices used to integrate implicitly the equations of motion in descriptor form.