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

Jian Zhang, Fred van Keulen, Alejandro M. Aragón*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
6 Downloads (Pure)

Abstract

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

Original languageEnglish
Article number114189
Number of pages29
JournalComputer Methods in Applied Mechanics and Engineering
Volume388
DOIs
Publication statusPublished - 2022

Keywords

  • Enriched finite element analysis
  • Interface-enriched generalized finite element method (IGFEM)
  • Level set
  • Linear elastic fracture mechanics
  • Stress recovery technique
  • Topological derivatives

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