Numerical modeling of rock failure under dynamic loading with polygonal elements

Polygonal finite elements are gaining an increasing attention in the computational mechanics literature, but their application in rock mechanics is very rare. This paper deals with numerical modeling of rock failure under dynamic loading based on polygonal finite elements. For this end, a damage-viscoplastic constitutive model for rock based on the Mohr-Coulomb criterion with the Rankine criterion as a tensile cutoff is employed and implemented with the polygonal finite element method. Moreover, the mineral mesostructure or rock is described by randomly mapping groups of polygonal elements representing the constituent minerals into a global mesh and assigning these groups with the corresponding mineral material properties. The performance of the polygonal elements is compared with that of the linear and quadratic triangular and bilinear quadrilateral elements in numerical simulations of controlled shear band formation under uniaxial compression and lateral splitting failure in the dogbone tension test. Numerical simulations of uniaxial tension and compression tests as well as dynamic Brazilian disc test under increasing loading rates demonstrate that the present approach predicts the correct failure modes as well as the dynamic increase in strength of rock.