Gradient concepts for evolution of damage

While low-order measures of damage have sufficed to describe the stiffness of bodies with distributed voids or cracks, such as the void volume fractio n or the crack density tensor of Vakulenko, A.A., Kachanov, M., 1971. [Inz. AN SSSR., Mekhanika Tverdogo Tela (Mech. Solids) 6 (4), 159], addressing t he growth of distributed defects demands a more comprehensive description o f the details of defect configuration and size distribution. Moreover, inte raction of defects over multiple length scales necessitates a methodology t o sort out the change of internal structure associated with these scales. T o extend the internal state variable approach to evolution, we introduce th e notion of multiple scales at which first and second nearest-neighbor effe cts of nonlocal character are significant, similar to homogenization theory . Further, we introduce the concept of a cutoff radius for nonlocal action associated with a representative volume element (RVE), which exhibits stati stical homogeneity of the evolution, and flux of damage gradients averaged over multiple subvolumes. In this way, we enable a local description at len gth scales below the RVE. The mean mesoscale gradient is introduced to refl ect systematic differences in size distribution and position of damage enti ties in the evolution process. When such a RVE cannot be defined, the evolu tion is inherently statistically inhomogeneous at all scales of reasonable dimension, and the concept of macroscale gradients of internal variables is the only recourse besides micromechanics. Based on a series of finite elem ent calculations involving evolution of 2D cracks in brittle elastica arran ged in random periodic arrays, we examine the evolution of the mean mesosca le gradients and note some preliminary implications for the utility of such an approach. (C) 1999 Published by Elsevier Science Ltd. All rights reserv ed.