Fracture model of brittle and quasibrittle materials and geomedia

Abstract

A general model and a unified mathematical formalism are proposed for description of inelastic deformation and fracture of any solids, where brittle or plastic, as their evolution in effective force fields. Loaded solids and media are considered as nonlinear dynamic systems. One of the main tasks of the work is to show that if deformation and fracture of a strong medium is treated as its evolution in effective force fields, numerical solutions of equations of solid mechanics do demonstrate the fundamental properties of nonlinear dynamic systems—self-organized criticality and two-stage evolution (a rather slow quasistationary stage and a superfast catastrophic stage or a blowup mode). The model is tested by simulation of fracture of quasibrittle composites under axial compression. Calculations are also presented for the now developing tectonic flows and seismic processes in Central Asia, including the Baikal rift zone and the Altai-Sayany folded region. It is shown that numerical solutions of all examined problems of inelastic deformation and fracture demonstrate self-organized criticality of loaded media, including peculiarities of slow dynamics and spatial-temporal migration of deformation activity, and as well as two-stage fracture: comparatively slow quasi-equilibrium damage accumulation and superfast catastrophic fracture. The predicted seismic events obey the Gutenberg-Richter law.