Fracture-based shape optimization built upon the topological derivative

Kazem Alidoost, Felipe Fernandez, Philippe H. Geubelle, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


In Silva et al. (2011) and Alidoost et al. (2020), the authors developed an approximation of the energy release rate field associated with a small edge or surface crack at any boundary location and with any orientation using the topological derivative. The approximation is computationally attractive because it requires only a single analysis on the non-cracked domain in contrast with conventional boundary-element and finite-element-based methods, which require a separate and costlier analysis for each crack length-location-orientation combination. In this work, a shape optimization scheme for fracture-resistant structures is developed using the energy release rate approximation. In the gradient-based optimization scheme, the domain and its boundary are defined implicitly using level-set functions. The level-set functions of arbitrary geometries are constructed using Boolean operations from the level-set functions of simple primitives. This geometrical representation has the dual advantage of (i) allowing shapes to intersect and/or separate during the optimization and (ii) simplifying the computation of the shape sensitivities.

Original languageEnglish (US)
Article number114994
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - May 15 2022


  • Energy release rate
  • Fracture
  • Level-set function
  • Shape optimization
  • Topological derivative

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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