Analysis of three-dimensional fracture mechanics problems: A two-scale approach using coarse-generalized FEM meshes

• Published in: International journal for numerical methods in engineering Vol. 81; no. 3; pp. 335 - 365
• Main Authors: Kim, D.-J., Pereira, J. P., Duarte, C. A.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 15.01.2010; Wiley
• Subjects: Boundary conditions; Computational techniques; Dirichlet problem; Exact sciences and technology; extended FEM; Finite element method; fracture; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); generalized FEM; global-local analysis; Mathematical analysis; Mathematical methods in physics; Mathematical models; multiscale; Physics; small cracks; Solid mechanics; Solution space; Structural and continuum mechanics; Unity; Neumann problem; Rupture; extended FEM; global-local analysis; Modeling; Adaptive method; Global solution; Global local method; fracture; Finite element method; Short crack; Boundary value problem; generalized FEM; small cracks; Dirichlet problem; Unity partition; multiscale; Structural analysis; eXtended Finite Element Method
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2690

This paper presents a generalized finite element method (GFEM) based on the solution of interdependent global (structural) and local (crack)‐scale problems. The local problems focus on the resolution of fine‐scale features of the solution in the vicinity of three‐dimensional cracks, while the global problem addresses the macro‐scale structural behavior. The local solutions are embedded into the solution space for the global problem using the partition of unity method. The local problems are accurately solved using an hp‐GFEM and thus the proposed method does not rely on analytical solutions. The proposed methodology enables accurate modeling of three‐dimensional cracks on meshes with elements that are orders of magnitude larger than the process zone along crack fronts. The boundary conditions for the local problems are provided by the coarse global mesh solution and can be of Dirichlet, Neumann or Cauchy type. The effect of the type of local boundary conditions on the performance of the proposed GFEM is analyzed. Several three‐dimensional fracture mechanics problems aimed at investigating the accuracy of the method and its computational performance, both in terms of problem size and CPU time, are presented. Copyright © 2009 John Wiley & Sons, Ltd.