Spallation analysis with a closed trans-scale formulation of damage evolution

A closed, trans-scale formulation of damage evolution based on the statistical microdamage mechanics is summarized in this paper. The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage. The spallation in an aluminium plate is studied with this formulation. It is found that the damage evolution is governed by several dimensionless parameters, i.e., imposed Deborah numbersDe ^* andDe, Mach numberM and damage numberS. In particular, the most critical mode of the macroscopic damage evolution, i.e., the damage localization, is determined by Deborah numberDe ^*. Deborah numberDe ^* reflects the coupling and competition between the macroscopic loading and the microdamage growth. Therefore, our results reveal the multi-scale nature of spallation. In fact, the damage localization results from the nonlinearity of the microdamage growth. In addition, the dependence of the damage rate on imposed Deborah numbersDe ^* andDe, Mach numberM and damage numberS is discussed. The project supported by the National Natural Science Foundation of China (10172084, 10232040, 10232050, 10372012, 10302029) and the Special Funds for Major State Research Project (G200077305)