Fiber Bundle Models for Composite Materials

In this paper we will outline the advantages of using fiber bundles in modeling disordered materials. We will present the main aspects of classical fiber bundle models (FBMs) and highlight their ability to capture some essential aspects of composite materials. We then present some extensions of the classical FBM, modifying the way of interaction of fibers, failure law, deformation state and constitutive behavior. The subclasses of FBMs which we generate in this way, i.e., the variable range of interaction model, the continuous damage FBM, the beam model, and the plastic FBM, will turn out to overcome some of the limitations of classical FBMs. We will discuss the characteristic dynamics of these model systems and give references to experiments.