Application of variational inequalities in problems of dynamics of elastic-plastic, bulk and porous media

Based on the original formulation of the flow theory equations in the form of variational inequalities for hyperbolic operators, the problem of generalized solutions with strong discontinuities in the dynamics of elastic-plastic media is investigated. Using the method of variational inequalities, a general method of constructing mathematical models of rheologically complex materials (soils, rocks, fibrous composites) that resist stretching and compression in different ways has been developed. New models of structurally inhomogeneous (blocky, loose, porous) media have been created, the fundamental difference between which and existing models is their thermodynamic correctness. Computational algorithms and programs have been developed that implement the proposed mathematical models in dynamics problems using high-performance computing on multiprocessor computers.