An Interface-Enriched Topology Optimization for Mitigating the Effect of Surface Flaws in 3-D Brittle Solids

  • Kosta, Majd (Delft University of Technology)
  • Liu, Shangru (Delft University of Technology)
  • Aragón, Alejandro (Delft University of Technology)

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This work is concerned with the computational design of three-dimensional structures with enhanced resistance to brittle fracture. Existing fracture-aware topology optimization approaches typically assume preexisting cracks and optimize the structural layout to mitigate their detrimental effects. A more realistic and robust design strategy should instead account for the possibility of cracks nucleating anywhere along the solid boundary. However, performing a separate finite element analysis for every potential crack location and orientation is computationally intractable. In this talk, we introduce an interface-enriched topology optimization framework that overcomes this limitation by combining the Interface-enriched Generalized Finite Element Method (IGFEM) with topological derivatives. The structural topology is represented by a level set function parameterized using radial basis functions, enabling precise geometric control [1, 2]. Potential cracks are assumed to nucleate at enriched nodes distributed along material boundaries, and their associated energy release rates are evaluated efficiently using topological derivatives. As a result, the fracture driving forces for all admissible cracks are obtained from a single enriched finite element analysis of the uncracked configuration. The optimization objective aggregates the energy release rates using a p-mean function, promoting designs with globally improved fracture resistance. Three-dimensional numerical examples demonstrate the ability of the proposed framework to generate topologies that are robust against crack nucleation in arbitrary locations and directions. [1] Sanne J. van den Boom, Jian Zhang, Fred van Keulen, and Alejandro M. Aragón. An interface-enriched generalized finite element method for level set-based topology optimization. Structural and Multidisciplinary Optimization, 63(1):1–20, 2021. [2] Jian Zhang, Fred van Keulen, and Alejandro M. Aragón. On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach. Computer Methods in Applied Mechanics and Engineering, 388:114189, 2022.