损伤统计演化方程的性质和数值模拟

通过对一种含成核尺寸效应的损伤统计演化方程性质的分析和数值模拟，揭示了损伤率主要是由微损伤在二维相空间中的前沿的运动所决定的这也就是Kachanov提出的损伤率演化方程的物理基础数值结果进一步显示了含成核尺寸效应模型在损伤发展上与-维模型的区别而且，由几种形式的细观动力学算出的损伤率与损伤的关系简单，可近似拟合为宏观上封闭的形式

PROPERTIES OF THE STATISTICAL DAMAGE EVOLUTION EQUATION AND ITS NUMERICAL SIMULATION

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.