Numerical solution of boundary-value problems for quasistatical flow of viscoplastic medium with negative strain rate sensitivity

An integrable nonlinear viscoplastic model with metastable strain rate dependence is of interest for describing the spatial autowave processes in the active media. The procedure for integrating the Cauchy, Goursat and mixed boundary-value problems has been developed for nonlinear equations of quasistatical flow of these media in their hyperbolicity area. Each problem is decoupled into two non-interacted subproblems which are solved in parallel. These subproblems are solved numerically with the aid of the noniterative methods developed for perfectly plastic solids. The formulations of nonclassical boundary-value problems with free and interphase boundaries are discussed.