Fourth order phase-field model for local max-ent approximants applied to crack propagation

Fatemeh Amiri, Daniel Millán, Marino Arroyo, Mohammad Silani, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


We apply a fourth order phase-field model for fracture based on local maximum entropy (LME) approximants. The higher order continuity of the meshfree LME approximants allows to directly solve the fourth order phase-field equations without splitting the fourth order differential equation into two second order differential equations. We will first show that the crack surface can be captured more accurately in the fourth order model. Furthermore, less nodes are needed for the fourth order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.

Original languageEnglish
Pages (from-to)254-275
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2016 Dec 1


  • Fourth order phase-field model
  • Fracture
  • Local maximum entropy
  • Second order phase-field model

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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