Topology optimization of structures guarding against brittle fracture via peridynamics-based SIMP approach

Fracture resistance of structures consisting of brittle materials is significantly important in engineering practice. In this work, we explore the application of peridynamics (PD) in the optimization of structures against brittle fracture. A fracture resistance topology optimization scheme under the PD-based analysis framework is proposed, where two fracture-based strategies are adopted to improve the structural fracture behavior. The first one sets the conventional fracture energy as a constraint. While the second constraint is the bond stretch established on the unique concept “bond” of the PD framework, which smoothly transfers the energy-based fracture resistance control to an intuitive and mathematically tractable geometric expression. The topology optimization is carried out under the SIMP framework, where densities are assigned to the bonds via material points to represent the topology changes and crack generation. Numerical examples and experiments demonstrate that the proposed strategies can guarantee the safety of the optimized structure against the occurrence of fracture failure.