A multiscale separated representation to compute the mechanical behavior of composites with periodic microstructure

The requirements for advanced numerical computations are very high when studying the multiscale behavior of heterogeneous structures such as composites. For the description of local phenomena taking place on the microscopic scale, the computation must involve a fine discretization of the structure. This condition leads to problems with a high number of degrees of freedom that lead to prohibitive computational costs when using classical numerical methods such as the finite element method (FEM). To overcome these problems, this paper presents a new domain decomposition method based on the proper generalized decomposition (PGD) to predict the behavior of periodic composite structures. Several numerical tests are presented. The PGD results are compared with those obtained using the classical finite element method. A very good agreement is observed.