Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of Newton's iteration

Fei Zhang, Weizhang Huang, Xianping Li, Shicheng Zhang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the moving mesh finite element method is able to adaptively concentrate the mesh elements around propagating cracks and handle multiple and complex crack systems.

Original languageEnglish (US)
Pages (from-to)127-149
Number of pages23
JournalJournal of Computational Physics
Volume356
DOIs
StatePublished - Mar 1 2018
Externally publishedYes

Keywords

  • Brittle fracture
  • Finite element method
  • Mesh adaptation
  • Moving mesh
  • Newton's iteration
  • Phase-field model

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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