A lattice Boltzmann model of statistical evolution of microvoids

A lattice Boltzmann model is proposed for the simulation of the statistical evolution of numerous microvoids under high stress triaxiality subjected to dynamic loadings. It considers the size distribution of microvoids during ductile fracture based on the balance law of microvoids’ number. A series of lattice Boltzmann equations governing the statistical evolution of microvoids are derived by using distribution function and multi-scale technique. Numerical results show that after a given time of evolution, microvoids in rate-sensitive materials are small and compact, whereas microvoids in rate-insensitive materials appear to be big and sparse, and the porosity in rate-insensitive material increases faster than that in rate-sensitive material. These numerical results might put insight into the mechanism of ductile fracture.