2-DIMENSIONAL ELASTIC COMPLIANCES OF MATERIALS WITH HOLES AND MICROCRACKS

Recent work has reported the independence of the effective Young's mod ulus, E, of a two-dimensional (2D) isotropic matrix containing holes f rom the matrix material Poisson's ratio, v(m), if the effective medium remains isotropic. The present work gives the explicit relations betw een the effective and matrix elastic properties for an isotropic 2D ma trix containing given holes and microcracks of any density, sire, shap e, distribution, and orientation in either isotropic or anisotropic ar rangement. To this general case, it is rigorously proved that E(m)H, i .e. the damage compliance H (which is the difference S - S-m between t he effective compliance S and the matrix compliance S-m) multiplied by the matrix Young's modulus E(m) is independent from both E(m) and the matrix material Poisson's ratio v(m). Consequently, the effective You ng's modulus is independent of v(m); and the dependent relations of th e effective shear and area bulk moduli on the matrix material Young's shear, area bulk moduli and Poisson's ratio are given. We also show th at the 2D elastic properties of an isotropic or anisotropic solid can be written in terms of the area bulk modulus and the orientation distr ibution function of the extension modulus.