On multi-scale approaches to composites and heterogeneous solids with damage.

The explosive increase in computational power and the paradigm of computer-based engineering practice have prompted analyses that claim to carry knowledge of material physics at small scales to the performance observed at the structural level. This hierarchical multi-scale approach has logical appeal and some mathematical formulation to support it for heterogeneous solids. However, when such solids suffer damage in the form of multiple cracks, the length scale hierarchy is no longer fixed or simple. Connecting multiple scales is then a challenge that needs addressing for given material systems, such as composite laminates, accounting for the pertinent damage. This paper describes damage in fiber-reinforced composites, illustrating the characteristic length scales of damage and their relationship with the fixed scales of heterogeneities. Hierarchical versus top-down approaches are discussed and a case is made for the so-called synergistic approach that combines continuum damage mechanics and micro-damage mechanics. [ABSTRACT FROM AUTHOR]