Effective properties of materials with random micro-cavities using special boundary elements

In this work, a general boundary element procedure is proposed to obtain the effective elastic tensor of solids containing randomly distributed micro-cavities in terms of its primary elastic properties. The average-field theory and a special boundary element formulation are combined to carry out a statistical analysis on the numerical results obtained for a Representative Volume Element (RVE). The two-dimensional isotropic material is simulated as a homogeneous matrix containing cylindrical holes. In the proposed implementation each hole boundary is modeled with a single boundary element. The average variables of the micro-field are evaluated using boundary-only data, which leads to a formulation particularly suitable for Boundary Element Methods. Expressions for effective elastic properties as a function of the micro-fields for both isotropic and transversally isotropic hypothesis are derived. Finally, the methodology is illustrated with some application examples and the results are compared with analytical and experimental results.