Damage and Smeared Crack Models

Abstract

Continuum damage mechanics is a constitutive theory that describes the progressive loss of material integrity due to the propagation and coalescence of microcracks, microvoids, and similar defects. These changes in the microstructure lead to a degradation of material stiffness observed on the macroscale. The term “continuum damage mechanics” was first used by Hult in 1972 but the concept of damage had been introduced by Kachanov already in 1958 in the context of creep rupture (Kachanov, 1958) and further developed by Rabotnov (1968); Hayhurst (1972); Leckie and Hayhurst (1974). The simplest version of the isotropic damage model considers the damaged stiffness tensor as a scalar multiple of the initial elastic stiffness tensor, i.e., damage is characterized by a single scalar variable. A general isotropic damage model should deal with two scalar variables corresponding to two independent elastic constants of standard isotropic elasticity. More refined theories take into account the anisotropic character of damage; they represent damage by a family of vectors (Krajcinovic and Fonseka, 1981), by a second-order tensor (Vakulenko and Kachanov, 1971) or, in the most general case, by a fourth-order tensor (Chaboche, 1979). Anisotropic formulations can be based on the principle of strain equivalence (Lemaitre, 1971), or on the principle of energy equivalence (Cordebois and Sidoroff, 1979) (the principle of stress equivalence is also conceptually possible but is rarely used).