Effective elastic properties of 2-D solids with circular holes: numerical simulations

In order to evaluate the reliability and precision of the existing approximate micromechanically-based theoretical schemes for the prediction of the effective elastic properties of a sheet containing holes, numerical simulations have been carried out. The boundary-element method has been adopted in numerical simulations on account of its numerical precision and other remarkable merits. First, the relationships between effective elastic properties of 2-D solids with random circular holes and the volume fraction of holes have been studied. Furthermore, to investigate the influence of the interaction between holes on the effective material moduli of 2-D solids, another kind of model with normally distributed holes has been analyzed. By comparing computational results with the theoretical solutions, the presently existing theoretical methods have been comprehensively evaluated. Furthermore, the effects of two parameters in the normal distribution function on the effective material moduli have been investigated in detail.