中文摘要：

Damage and failure due to distributed microcracks or microvoidsare on the challenging frontiers of solid mechanics. This appeals strongly to toolsnot yet fully developed in continuum damage mechanics, in particular to irreversiblestatistical thermodynamics and a unified macroscopic equations of mechanics andkinetic equations of microstructural transformations. This review provides the stateof the art in statistical microdamage mechanics. (1) It clarifies on what level of approximation continuum damage mechanicsworks. Particularly, D-level approximation with dynamic function of damage appearsto be a proper closed trans-scale formulation of the problem. (2) It provides physical foundation of evolution law in damage mechanics. Es-sentially, the damage-dependent feature of the macroscopic evolution law is due tothe movement of microdamage front, resulting from microdamage growth. (3) It is found that intrinsic Deborah number D, a ratio of nucleation rateover growth rate of microdamage, is a proper indication of critical damage in damagemechanics, based on the idea of damage localization. (4) It clearly distinguishes the non-equilibrium damage evolution from equilib-rium phase transition, like percolation. Finally, some comments on its limitations are made.

英文摘要：

Damage and failure due to distributed microcracks or microvoids are on the challenging frontiers of solid mechanics. This appeals strongly to tools not yet fully developed in continuum damage mechanics, in particular to irreversible statistical thermodynamics and a unified macroscopic equations of mechanics and kinetic equations of microstructural transformations. This review provides the state of the art in statistical microdamage mechanics. (1) It clarifies on what level of approximation continuum damage mechanics works. Particularly,D-level approximation with dynamic function of damage appears to be a proper closed trans-scale formulation of the problem. (2) It provides physical foundation of evolution law in damage mechanics. Essentially, the damage-dependent feature of the macroscopic evolution law is due to the movement of microdamage front, resulting from microdamage growth. (3) It is found that intrinsic Deborah numberD *, a ratio of nucleation rate over growth rate of microdamage, is a proper indication of critical damage in damage mechanics, based on the idea of damage localization. (4) It clearly distinguishes the non-equilibrium damage evolution from equilibrium phase transition, like percolation.