The plasticity part of the model is based on the effective stress formulation and employs the Mohr-Coulomb yield criterion with the Rankine criterion as a tensile cut-off. The phenomenological damage part of the model is based on the orthotropic damage formulation in tension and the isotropic damage in compression. Using the effective stress formulation the plasticity and damage processes can be separated so that the trial stress is first returned to the yield surface and then the damage effects are computed independently. Finally, the nominal stress is computed using the stress based projection operator method since it provides a means for the treatment of the microcrack closure-reopening effects, i.e. the switching between the tensile and compressive damage modes as well.

The damage evolution law in tension is based on the specific fracture energy which provides the mesh objective energy dissipation. A novel method for calibrating the damage evolution law in compression is presented. Thereby, the exponential type of damage evolution law depends on the confining pressure as the asymptotic parameter is identified with the degradation index concept of Fang and Harrison [1].

The stress integration and the damage computation are performed in the principal stress space. Non-associative flow rules are used both in compression and tension. In tension a non-associative flow rule produces the correct constitutive response (no stresses orthogonal to the axial direction) in uniaxial tension. Due to the linearity of the Mohr-Coulomb criterion and the softening/hardening rule no iteration is needed in the stress integration as both the plastic and damage parts are explicit.

The heterogeneity of rock is taken into account statistically by assuming that the stiffness and strength parameters conform to a Weibull distribution. The indenter is modeled as a deformable body and its impact to the rock sample is modeled by contact mechanics. The contact constraints are imposed exactly by the forward increment Lagrange multiplier method which is compatible with explicit time integrators. The governing finite element discretised equations of motion are solved with the explicit modified Euler time integrator. Finally, a numerical example of dynamic indentation is solved in order to demonstrate the performance of the model.

1

Z. Fang, J.P. Harrison, "A mechanical degradation index for rock", Int. J. Rock Mech. Min. Sci., 38, 1193-1199, 2001. doi:10.1016/S1365-1609(01)00070-3

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