A FFT solver for variational phase-field modeling of brittle fracture

Yang Chen, Dmytro Vasiukov, Lionel Gélébart, Chung Hae Park

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62 Citations (SciVal)


The variational phase-field method is an attractive non-local approach of modeling fracture in heterogeneous materials. However, these materials usually require a fine mesh to resolve the fracture process zone. Consequently, the standard finite element solver becomes cumbersome due to the large number of elements in applications with highly heterogeneous materials. Motivated by this limitation, an algorithm based on FFT methods has been introduced in this paper to solve the phase-field model of brittle fracture. Relying on a staggered update scheme, the proposed algorithm solves the fracture problem and mechanical problem separately, both using the FFT technique. It inherits the advantages of classical FFT methods in terms of simplicity of mesh generation and parallel implementation. Introduced within a FFT-based code “AMITEX” it takes the advantage of massively parallel capabilities associated with a distributed memory implementation. The characteristics of the proposed method are analyzed in a single edge notched specimen benchmark. Representative numerical examples demonstrate that the proposed FFT solver is capable of predicting different crack modes and complex crack configuration, such as crack interaction, branching and coalescence. Finally, a model of an idealized continuous fiber composite with void involving over 32 million voxels is solved, illustrating the potential of the FFT solver in large-scale problems.

Original languageEnglish
Pages (from-to)167-190
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Early online date18 Feb 2019
Publication statusPublished - 1 Jun 2019

Bibliographical note

Funding Information:
The authors would like to acknowledge the European Union (European Regional Development Fund, ERDF/FEDER) , the French state and the Hauts-de-France Region Council for partly funding the ELSAT2020 by CISIT project (POPCOM action). Our gratitude is to Dr. Julien Derouillat from Maison de la Simulation for his contribution to the improvement of AMITEX code. We also would like to thank Prof. James Marrow from Oxford university for the language proofreading of the manuscript.


  • Brittle fracture
  • FFT method
  • Fixed-point algorithm
  • 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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