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

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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.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 2122 Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL, 61801, USA

    J. P. A. Pereira & C. A. Duarte

  2. Department of Architectural Engineering, Kyung Hee University, Engineering Building, 1 Sochon-Dong Kihung-Gu, Yongin, Kyunggi-Do, 446-701, Korea

    D.-J. Kim

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  1. J. P. A. Pereira
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  3. C. A. Duarte
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Correspondence to C. A. Duarte.

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Pereira, J.P.A., Kim, DJ. & Duarte, C.A. A two-scale approach for the analysis of propagating three-dimensional fractures. Comput Mech 49, 99–121 (2012). https://doi.org/10.1007/s00466-011-0631-4

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