### Abstract

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 language | English |
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Pages (from-to) | 681-703 |

Number of pages | 23 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 53 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Mar 1 |

Externally published | Yes |

### Keywords

- 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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## Cite this

*Journal of the Mechanics and Physics of Solids*,

*53*(3), 681-703. https://doi.org/10.1016/j.jmps.2004.08.005