Multi-material topology optimization design for continuum structures with crack patterns

This study proposes a compliance multi-material topology optimization design of continuum structures with the dependence of crack patterns. Multi-material optimal topology and shape are produced as an alternative to prevent the propagation of crack patterns. The extended finite element method (X-FEM) is used to be a mechanical description approach of strong discontinuity state such as the present cracks. Heaviside enrichment and linear elastic asymptotic displacement fields are added to the finite element approximation without mesh generation near initial cracks. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. The mathematical formulation of multi-material topology optimization problem solving minimum structural compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Several numerical examples considering the number, length, angle and location of cracks with or without retrofitting solid passive multi-material verify the efficiency of the present design method using of multiple materials and with the dependence of different crack patterns occurring at continuum structures.