homogenization

Understanding the non-elastic behavior of demolished rock in the rock structures, especially after maximum resistance, is required for the stability analysis of the rocky structure. Mechanical failure theory is a method for analyzing the behavior of rocks, especially after maximum resistance. Methods based on fracture mechanics consider the behavior of the rock well, such as reducing load capacity after maximum resistance and elastic rigidity. In this research, a microstructural failure model for open and closed friction microcrack is considered, taking into account the coupling between frictional slip and damage. Therefore, the basic concepts of mechanical mechanics failure are presented first. To calculate the effect tensor, the Ponte-Castaneda and Willis (1995) homogenization pattern has been used. Then, the formulation of this model was coded in FLAC software environment and the micromechanics damage behavior model developed in the FLAC software environment was called as a new behavioral model. In order to use the developed model and validate it on a laboratory scale, a axial compressive strength test on limestone was used as the basis, and its results with acceptable numerical model were acceptable.

In last decades, phenomenological constitutive damage models were used by many researchers to study for brittle failure of rock materials. Most phenomenological constitutive damage models utilize the irreversible thermodynamic principles to take into account the damage processes in brittle rock materials. Since this type of damage model do not consider the actual physical phenomena in the damage process, the micromechanical damage models are often used to consider the actual physical mechanisms in micro-scales specially in nucleation and propagation of wing-cracks from pre-existing flaws tips. Frictional sliding on closed micro-cracks surfaces leads to inelastic deformation and wing-cracks nucleation from flaw tips. Because of the different distribution of size and orientation of microflows in the rock materials, under dynamical loading, all of the pre-existing micro-flaws in the rock are activated and propagated. The interaction of micro-cracks with other and coalescence of these micro-cracks play a key role in accumulation of damage and macro-scale fracture plane formation in the rock. The various homogenization schemes e.g. Mori-Tanaka, Self-consistent and Ponte-Castandea were applied for calculation of equivalent mechanical parameters of materials. In this study, the Self-consistent scheme (SCS) was used for homogenization of rock sample under uniaxial dynamic compressive loading. The developed model was programmed and used as a separate and new constitutive model in the commercial finite difference software (FLAC).The dynamic compressive test of a brittle rock was simulated numerically and the stress-strain curves under dynamic loading were simulated and compared with one another. The proposed model predicts a macroscopic stress-strain relation and a peak stress (the materials compressive strength) with an associated transition strain rate beyond which the compressive strength of the material becomes highly strain rate sensitive. The results also show that as the strain rate increases, the peak strength increases and the damage evolution becomes slower.