Effective Elastic Moduli of Cracked Solid and Application to Functionally Graded Material

In this paper, effective moduli of cracked solid material were investigated. An analytical approach is discussed for a cracked solid containing randomly oriented inclusions by using elastic potential and a standard tensorial basis. A numerical simulation of the testing of mechanical responses of samples of cracked solid material (porous material) is also carried out. The numerical scheme in this work will focus mainly on numerical modeling of the observed behavior, in particular, the dependence of the macroscopic material properties on the porosity. This numerical scheme is also applied to functionally graded material (FGM). Effective elastic constants for FGM samples with various crack orientations and densities were calculated by both the boundary numerical integration method and the domain numerical integration method.