Abstract.To study the mechanical response of brittle porous materials at mesoscale, porous samples were generated and their deformation was numerically modelled. Two types of pore space morphology such as overlapping spherical pores and overlapping spherical solids were explicitly considered. For deformation modelling, an evolutionary approach including the nonlinear constitutive equations used to describe damage accumulation and its impact on the degradation of the solid frame strength properties was applied. The numerical results have shown that an average stress-strain diagram is sensitive to pore morphology as well as porosity.

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 systemsself-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 GutenbergRichter law.

The fracture of brittle specimens with an initial crack under uniaxial compression is studied experimentally. The effect of the crack orientation on the fracture of the specimens is examined. It is established that the crack nucleates and advances mainly in the loading direction (longitudinal fracture being predominant). The brittle material is modeled taking into account the difference between the compressive and tensile strengths of the material, the accumulation of damage, and the degradation of strength. The results obtained with the model in analyzing the fracture of brittle specimens with an initial crack under uniaxial compression are in satisfactory agreement with experimental data

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