Eulerian modeling of compressible multicomponent elastic materials

An Eulerian numerical model is developed for calculating dynamic processes in multimaterial elastic media. Accurate and correct description of the interaction of materials on the surface of the interface and the dynamics of the interface itself is inevitably required. Problems with large deformation of the interface cause serious difficulty when using Lagrangian numerical methods as they lead to strong distortion of the computational grid and loss of the accuracy. For such problems, so-called diffuse interface models are more preferred allowing one to track the interface and calculate the propagation of perturbations due to the interaction of materials on a fixed grid with a larger degree of accuracy. However, most of such models consider the dynamics of the medium in the hydrodynamic approach. The present paper is devoted to the extension of the class of diffuse interface models to the elastoplastic rheology of materials. The two-material model proposed is basically the extension of the hydrodynamic Baer–Nunziato two-phase model to hypoelastic materials. Numerical results demonstrate the capabilities of the model to accurately simulate wave processes in multimaterial media.