Micromechanical damage model for brittle materials under dynamic uniaxial compressive loading

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.