A two-scale approach for the analysis of propagating three-dimensional fractures

  • Authors:

  • J. P. Pereira;D. -J. Kim;C. A. Duarte

  • Affiliations:

  • Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, USA 61801;Department of Architectural Engineering, Kyung Hee University, Yongin, Kyunggi-Do, Korea 446-701;Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, USA 61801

  • Venue:
  • Computational Mechanics
  • Year:
  • 2012

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Abstract

This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution--a smooth coarse-scale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in neighborhoods of cracks. Boundary conditions for the local problems are provided by the available solution at a crack growth step. The methodology enables accurate modeling of 3-D propagating cracks on meshes with elements that are orders of magnitude larger than those required by the FEM. The coarse-scale mesh remains unchanged during the simulation. This, combined with the hierarchical nature of GFEM shape functions, allows the recycling of the factorization of the global stiffness matrix during a crack growth simulation. Numerical examples demonstrating the approximating properties of the proposed enrichment functions and the computational performance of the methodology are presented.