Explicit-Implicit Numerical Scheme for Problems in the Dynamics of Elastoviscoplastic Media with Softening

An explicit-implicit scheme is constructed for the numerical solution of the system of equations governing an elastoviscoplastic continuous medium with softening. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations, which contain a small relaxation time parameter in the denominator of the nonlinear free terms. Accurate formulas for correcting the stress deviators after the elastic computation step are derived in the case of a linear viscosity function and a nonlinear softening law. The resulting solutions of the implicit approximation for the stress deviators of the elastoviscoplastic system admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of numerical solutions to ill-posed elastoplastic systems with softening.