Some remarks on gradient and nonlocal damage theories

Abstract

This chapter discusses the enriched damage theories in which the damage is coupled to (isotropic) elasticity. They can be related to nonlocal damage models in an integral format, their properties are in some cases quite different from those of nonlocal integral-type damage models, as has been shown by dispersion analyses and by a simple one-dimensional example. The standard damage theories and nonlocal damage theories in an integral format are described in the chapter. Based on the latter class of theories, a family of gradient-enhanced damage theories is derived in the chapter. For the particular case where higher-order gradients of a local equivalent strain are introduced, a refinement is described in the chapter, which remedies the problem of artificial widening of the damage zone in the progressive stages of the loading process. A description of the numerical implementation of this model is also presented in the chapter. A comparison is described between some gradient damage theories and a nonlocal damage theory in an integral format in the chapter.