Combining Maxwell's methodology with the BEM for evaluating the two-dimensional effective properties of composite and micro-cracked materials

Maxwell's methodology is combined with the boundary element method (BEM) for evaluating the two-dimensional effective elastic properties of composite, porous, and microcracked isotropic materials with periodic or random structure. The approach is based on the idea that the effective properties of the material can be deduced from the effects that a cluster of fibers, pores, or cracks embedded in an infinite matrix has on the far-fields. The fibers, pores, or cracks can have arbitrary shapes, sizes, and elastic properties, provided that the overall behavior is isotropic, and their effects are assumed to be the same as those of an equivalent circular inhomogeneity. The key aspect of the approach is to precisely account for the interactions between all the constituents in the cluster that represent the material in question. This is done by using the complex-variables version of the BEM to solve the problem of a finite cluster of fibers, pores or cracks embedded an infinite isotropic, linearly elastic matrix. The effective properties of the material are evaluated by comparing the far-field solutions for the cluster with that of the equivalent inhomogeneity. It is shown that the model adequately captures the influence of the micro-structure of the material on its overall properties.