Rheological Schemes -- Mathematical Apparatus -- Spatial Constitutive Relationships -- Limiting Equilibrium of a Material with Load Dependent Strength Properties -- Elastic-Plastic Waves in a Loosened Material -- Contact Interaction of Layers -- Results of High-Performance Computing -- Finite Strains of a Granular Material -- Rotational Degrees of Freedom of Particles.

This monograph contains original results in the field of mathematical and numerical modeling of mechanical behavior of granular materials and materials with different strengths. It proposes new models helping to define zones of the strain localization. The book shows how to analyze processes of the propagation of elastic and elastic-plastic waves in loosened materials, and constructs models of mixed type, describing the flow of granular materials in the presence of quasi-static deformation zones. In a last part, the book studies a numerical realization of the models on multiprocessor computer systems. The book is intended for scientific researchers, lecturers of universities, post-graduates and senior students, who specialize in the field of the deformable materials mechanics, mathematical modeling and adjacent fields of applied and calculus mathematics.