Proposal of FEM implemented with particle discretization for analysis of failure phenomena

Muneo Hori, Kenji Oguni, Hide Sakaguchi

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


A new method for numerical simulation of failure behavior, namely, FEM-β, is proposed. For a continuum model of a deformable body, FEM-β solves a boundary value problem by applying particle discretization to a displacement field; the domain is decomposed into a set of Voronoi blocks and the non-overlapping characteristic functions for the Voronoi blocks are used to discretize the displacement function. By computing average strain and average strain energy, FEM-β obtains a numerical solution of the variational problem that is transformed from the boundary value problem. In a rigorous form, FEM-β is formulated for a variational problem of displacement and stress with different particle discretization, i.e., the non-overlapping characteristic function of the Voronoi blocks and the conjugate Delaunay tessellations, respectively, are used to discretize the displacement and stress functions. While a displacement field is discretized with non-smooth functions, it is shown that a solution of FEM-β has the same accuracy as that of ordinary FEM with triangular elements. The key point of FEM-β is the ease of expressing failure as separation of two adjacent Voronoi blocks owing to the particle discretization that uses non-overlapping characteristic functions. This paper explains these features of FEM-β with results of numerical simulation of several example problems.

Original languageEnglish
Pages (from-to)681-703
Number of pages23
JournalJournal of the Mechanics and Physics of Solids
Issue number3
Publication statusPublished - 2005 Mar 1
Externally publishedYes


  • Discontinuous finite element method
  • Failure analysis
  • Non-overlapping shape functions
  • Particle modeling
  • Voronoi and Delaunay tessellation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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