Theoretical modeling of the dynamic tensile response of Laurentian granite using the dominant crack algorithm

Abstract

Dominant crack algorithm (DCA) is a statistical micromechanics model for the dynamic tensile response of brittle materials. In the DCA model, both microscopic and macroscopic material parameters are included to construct the constitutive relation, and the damage evolution is described by the growth of the dominant crack. In this study, the sensitivity analysis of the microscopic parameters (i.e. the characteristic volume size a, the initial crack size c0, and the crack velocity related parameter m) in the DCA model is conducted. The results demonstrate that the dynamic tensile strength is sensitive to the value of c0/a. Compared with the influence of the c0/a on the dynamic tensile strength, the dynamic tensile strength is less sensitive to the variation of the characteristic volume size a or the variation of the crack velocity related parameter m. Furthermore, the DCA model is applied to predict the dynamic tensile response of Laurentian granite (LG). A nonlinear regression method - Particle Swarm Optimization (PSO) - is utilized to optimize the values of the microscopic parameters. The results indicate that the dynamic tensile response of LG predicted by the DCA modeling has a good agreement with that obtained from the experiments. Therefore, the DCA modeling is valid and applicable to describe the dynamic tensile response and predict the dynamic tensile strength of rock-like materials.