Topology optimization of bi-material structures with Iso-XFEM

Iso-XFEM is a recently proposed evolutionary topology optimization method, which is based in the extended finite element method (XFEM). Similarly to XFEM, Iso-XFEM utilises the level set approach in order to achieve a high-resolution, smooth, and accurate representation of the design boundary using a fixed finite element mesh. Compared to conventional evolutionary and material density methods for topology optimization, such as SIMP and ESO/BESO, Iso-XFEM exhibits less pronounced mesh dependency, while it completely avoids checkerboard problems and the need for a postprocessing step to produce feasible structural forms. In the present study, IsoXFEM is extended in order to handle effectively topology optimization problems involving two materials, by introducing enrichment functions in conjunction with a XFEM approximation of the solution. This way, the material interface boundaries and its evolution can be accurately represented during the optimization process. A number of 2D and 3D test cases are presented to confirm the efficiency of the proposed method for the optimum design of bi-material structures.