Formulation for wave propagation in dissipative media and its application to absorbing layers in elastoplastic analysis using mathematical programming

In this article, we propose a new solution scheme for modeling elastoplastic problems with stress wave propagation in dissipative media. The scheme is founded on a generalized Hellinger–Reissner (HR) variational principle. The principle renders the discretized boundary-value problem into an equivalent second-order cone programming (SOCP) problem that can be resolved in mathematical programming using the advanced optimization algorithm—the interior point method. In such a way, the developed method not only inherits admirable features of the SOCP-based finite element method in solving elastoplastic problems but also enables the enforcement of absorbing layers (i.e., Caughey absorbing layer), which is essential in modeling stress wave propagation problems, to absorb wave energy. The proposed scheme is validated via the comparison between analytical and numerical results for seismic wave propagation in dissipative media. Its application to elastoplastic dynamic problems with stress wave propagation is also illustrated to demonstrate its efficiency