A combined viscoplastic damage-phase field model for rock fracture under dynamic loading

The phase field method captures tensile (mode I) fracturing of brittle materials but has serious challenges in uniaxial compression of heterogeneous materials like rock and concrete. In this paper, we mend this drawback by combining a phase field model for mode I fracture with a viscoplastic damage model to capture the shear banding in uniaxial compression of rock. In the present phase field formulation, the mode I fracture is driven by Rankine type of crack driving force, while the Mohr–Coulomb criterion is employed in the viscoplastic damage part of the model to capture the compressive/shear failure. As the model is designed for transient dynamic problems, strain rate sensitivity of rock is accommodated, here by a linear viscous term in both
the phase field and viscoplastic damage parts. The viscoplastic part is cast in the consistency format. The phase field variable and the damage variable operate, respectively, on the positive and negative parts of the principal stress returned to the (Mohr–Coulomb) yield surface. The performance of the model is demonstrated
in uniaxial tension and compression tests. Finally, the dynamic Brazilian disc test and punch-through shear tests are simulated for further validation. The model captures the strain rate sensitive direct and indirect tensile strength as well as the correct failure modes in these tests