REDUCED DEPENDENCE OF DEFECT COMPLIANCE ON MATRIX AND INCLUSION ELASTIC PROPERTIES IN 2-DIMENSIONAL ELASTICITY

In our other recent work (Zheng & Hwang 1996), we established the expl icit relations between the effective and the matrix elastic properties in two-dimensional (2D) elasticity, as the effective medium is compri sed of an isotropic and homogeneous matrix, microcracks and holes of v arious shapes. The present paper extends the above result to the case for a composite material comprising either isotropic or anisotropic ma trix and inclusions which have respectively continuously varying compl iances, and for a variety of interface conditions. It is shown that th e effective compliance depends upon a reduced list of the matrix and i nclusion material constants. In particular, when the matrix and inclus ions are all isotropic and respectively homogeneous, then E(m)H (i.e. the defect compliance H which is the difference, S - S-m, between the effective compliance S and the matrix compliance S-m multiplied by the matrix Young's modulus E(m)) has a reduced dependence upon the E(m)/E (I) and nu(m) - nu(I)E(m)/E(I) for the inclusion of Young's moduli EI and Poisson's ratios nu(I) and the matrix Poisson's ratio nu(m), rathe r than the full material constant list of E(I), nu(I), E(m), nu(m). Ap plications to various important types of matrix and inclusion material s are given. We also show that the generalized self-consistent method (Christenson & Lo 1919) provides solutions of the effective moduli for unidirectional fibre composites in compatible forms with the general dependence relations proved in the present paper.