A two-scale approach for the analysis of propagating three-dimensional fractures |
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Authors: | J P A Pereira D-J Kim C A Duarte |
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Affiliation: | (1) Department of Structural Engineering, Federal University of Minas Gerais, Av. Contorno, 842, 2?. andar, Centro, 30110-060 Belo Horizonte, MG, Brazil;(2) Graduate Program in Mechanical Engineering, Campus Universitrio - Trindade, Federal University of Santa Catarina, 88040-900 Florianpolis, SC, Brazil;(3) 2122 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL 61801-2352, USA |
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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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