Multiscale Modeling Of Functionally Graded Materials

In this paper, we considered the multiscale modelling and simulation offunctionally graded materials(FGM). FGM is a composite materials which could beapplied in many areas. First of all, we derived the macroscopic model from themicroscopic one for the materials with periodic microstructure. We carried out thecorresponding convergence analysis under the frame of homogenization. For gen-gral cases, we desigened the multiscale model under the frame of HeterogeneousMultiscale Method(HMM) and gave out the error estimate between the HMM so-lutions and the homogenization solutions under the assumption that there exists aperiodic microscale structure. At last, numerical experiments were carried out todemonstrate the accuracy of the methods.