Explicit-Implicit Schemes for Calculating the Dynamics of Elastoviscoplastic Media with a Short Relaxation Time

We consider the dynamic behavior of elastoviscoplastic media under the action of anexternal load. For the general case of a nonlinear viscosity function describing high-speedhardening, we construct an explicit-implicit calculation scheme of the second order ofapproximation that permits one to obtain a numerical solution of the original semilinearhyperbolic problem. A distinctive feature of this approach is that it does not use the method ofsplitting by physical processes. Despite this, an explicit computational algorithm was obtainedthat allows efficient implementation on modern computing systems.