PROPERTIES OF THE STATISTICAL DAMAGE EVOLUTION EQUATION AND ITS NUMERICAL SIMULATION
损伤统计演化方程的性质和数值模拟

Damage mechanics has become a very helpful tool for engineers to deal with failure problems. Actually the physical essence of damage is the population of distributed microdamage in a continuum element. When one intends to correlate the damage evolution to the mesoscopic dynamics of microstructure of a particular material, it becomes necessary to investigate the statistical evolution of distributed microdamage. Based on the analysis and numerical simulation of one kind of statistical damage evolution equation, we find that the rate of continuum damage is determined mainly by the movement of microdamage front of in two-dimension phase space. This concisely links continuum damage evolution to its underlying mesoscopic dynamics. Numerical simulations reveals the distinction between two models: model with nucleation effect and model without nucleation effect. Furthermore, it is demonstrated that the evolution law of damage, D can approximately be fitted into a closed expression on macroscopic level deduced from several mesoscopic dynamics.