Special finite element-based unit cell approaches for heterogeneous materials

To predict the overall structure properties of heterogeneous materials, the finite element (FE)- based multiscale unit cell approach (UCA) can be applied through the appropriate selection of representative volume element (RVE). On the basis of micromechanics and finite element method, this unit cell approach (UCA) is developed to obtain the averaged stress-strain results for a certain prescribed deformation history via finite element models with periodic boundary conditions. Unfortunately, the finite element models using traditional finite elements require the deliberate meshes to ensure the accuracy. The special finite element containing an internal inhomogeneity can be naturally applied in this occasion with the high accuracy for two dimensional multiscale modeling of heterogeneous materials, and there needs only one special element applied in the vicinity of the inhomogeneity. In this chapter, such two-dimensional special finite element-based unit cell approaches are presented, which can greatly simplify the modeling procedure and ensure high accuracy for multiscale modeling of heterogeneous materials.