The possibilities and limitations of the homogenized description of inelastic behavior of brittle porous materials under constrained conditions

The paper presents the results of studying inelastic deformation and fracture of microscopic regions of porous brittle materials under triaxial compression using the movable cellular automaton method. The study is focused on analyzing the applicability of the classical macroscopic criteria of plasticity and strength for the integral description of the mechanical response of microscopic representative volumes. We analyzed the dependence of the parameters of the integral mechanical response of the microscopic regions on the value of porosity, spatial distribution of pores and strength of the material in the skeleton walls. Main stages of the process of damage accumulation and growth in the skeleton walls and its manifestation in the integral inelastic response of the considered microscopic region are investigated by the example of the axial compression of the samples under constant lateral pressure. It is shown that the increase in the value of the lateral pressure leads to a change in the fracture type of the porous material from the elastic-brittle fracture to the formation of the shear localization zone (shear band) and then (at higher lateral pressures) to the spatially distributed cataclastic flow. The characteristic threshold values of the lateral pressure at which the failure mechanism starts to change, mostly depend on the sensitivity of the skeleton wall strength to the local pressure. The analysis of the simulation results showed that the conventional plasticity conditions (criteria) which take into account the contribution of the local average stress in the linear approximation, are able to adequately describe the response of the microscopic representative volumes of brittle porous materials under constrained conditions only from the beginning of inelastic deformation to the stage of the formation of the system of non-interacting relatively short cracks. It is important to note that the softening of the representative microvolumes of brittle porous materials under constrained conditions is concerned not with the loss of integrity of the sample, but with subsequent processes of forming the localized shear bands and pore collapse in the already fragmented material. This gives reason to believe that the experimentally determined strength of the constrained sample as the maximum resistance force may be significantly overestimated in comparison to the true value (corresponding to the fragmentation of the material). It is established that the conditions for the loss of integrity of brittle porous materials under constrained conditions are adequately described using the "linear" failure criteria with the parameters determined not by standard uniaxial compression/tension tests but by multiaxial compression tests.