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

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...

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Bibliographic Details
Published in:Computational mechanics 2012-01, Vol.49 (1), p.99-121
Main Authors: Pereira, J. P. A., Kim, D.-J., Duarte, C. A.
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Classical and Continuum Physics
Computational Science and Engineering
Computer simulation
Crack propagation
Cracks
Engineering
Finite element method
Fractures
Mathematical analysis
Original Paper
Shape functions
Stiffness matrix
Theoretical and Applied Mechanics
Three dimensional analysis
Three dimensional models
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Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-011-0631-4