Computation of impacts on elastic solids by methods of bicharacteristics
Computational Mechanics '88, 2, chapter 60, Springer Berlin Heidelberg, Berlin, Heidelberg, (1988)DOI: 10.1007/978-3-642-61381-4_452
Abstract
Shock waves, explosions, impacts or cavitation bubble collapses may generate stress waves in solids causing cracks or unexpected damage due to focussing, physical nonlinearity or interaction with existing cracks. There is a growing interest in wave propagation, which poses many novel problems to experimentalists and theorists. Wave propagation is mostly governed by hyperbolic PDEs. Numerical methods applicable to strong waves in solids, which are as powerful as the FEM e.g. applied to static or quasi-static problems, have not yet been evolved for multi dimensional problems. All state of the art methods for hyperbolic problems are based on the solution of the local wave propagation. They differ in the construction of the fundamental solution and thus in the treatment of singularities connected with any sharp wave front such as acceleration waves and shocks. For application to solids, the methods of bicharacteristics seem to be especially well suited, since fundamental solutions can be constructed in a straight forward way for various constitutive equations.