On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic mechanics assumptions for brittle materials. use level set function discretized by radial basis functions represent the and Interface-enriched Generalized Finite Element Method (IGFEM) obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from boundary, location of enriched nodes are added enhance finite element approximation. Instead performing multiple analyses evaluate energy release rates (ERRs) all potential cracks—a would be computationally intractable—we approximate them means topological derivatives after single analysis uncracked domain. ERRs then aggregated construct objective function, corresponding sensitivity formulation is derived analytically adjoint formulation. Several numerical examples demonstrate technique’s ability tailor resistance, including well-known benchmark L-shaped bracket multiple-loading problem obtaining structure anisotropy.