Energy release rate approximation for small surface cracks in three-dimensional domains using the topological derivative

Kazem Alidoost, Meng Feng, Philippe H. Geubelle, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review

Abstract

The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

Original languageEnglish (US)
Article number041004
JournalJournal of Applied Mechanics, Transactions ASME
Volume87
Issue number4
DOIs
StatePublished - Apr 2020

Keywords

  • Asymptotic analysis
  • Computational mechanics
  • Energy release rate
  • Failure criteria
  • Mixed mode fracture
  • Surface cracks
  • Topological derivative

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Energy release rate approximation for small surface cracks in three-dimensional domains using the topological derivative'. Together they form a unique fingerprint.

Cite this