A coupled model of asymmetric GIMP and tetrahedron CPDI based on the penalty contact algorithm for simulating dynamic rock splitting

Abstract

A coupled material point model (MPM) based on the asymmetric generalized interpolation material point (aGIMP) and the tetrahedron convected particle domain interpolation (CPDI-Tet4) was established to simulate the dynamic splitting of a rock Brazilian disc under small deformation. Furthermore, a boundary-based contact algorithm was developed to accurately describe the contact force between the split bar's aGIMP particles and the rock's CPDI-Tet4 particles. The proposed aGIMP technology enabled particles to move on a non-uniform background grid by changing the original basis functions. A good simulation effect was achieved. It was concluded that the rock particle size plays an important role in the accuracy of the contact algorithm. Two shear failure bands were generated near the contact zones first after the rock specimen reached the force equilibrium state, and then the four arc fracture surfaces grew from the two sides of the shear failure bands and coalesced to a radial fracture surface on the mid-cross section of the specimen. In addition, the tensile strength calculated by the MPM model exhibited the typical rate effect of rock material and was slightly lower than the practical tensile strength of the particle on the radial fracture surface.