An enriched dual boundary element method formulation for linear elastic crack propagation. (December 2020)

• Record Type: Journal Article
• Authors: Andrade, H.C.; Leonel, E.D.
• Is Part Of: Engineering analysis with boundary elements. Volume 121(2020)
• Page Start: 158
• Page End: 179
• Publication Date: 2020-12
• Subjects: Extended boundary element method -- Enriched formulations -- Linear elastic fracture mechanics -- Crack growth -- Coalescence; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.09.007
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: XBEM approach for efficient analysis of crack growth is proposed. Crack tip enrichment allows the direct evaluation of the SIFs. The proposed discontinuous enrichment avoids remeshing of existing elements. Point boundary conditions applied through enrichment of the traction approximation. The enriched formulation can be easily implemented into existing DBEM codes. Abstract: This study presents an eXtended Boundary Element Method (XBEM) formulation for simulating the linear elastic crack growth in two-dimensional domains. A displacement approximation enrichment based on the Williams first-order expansions is used to represent the near-tip square root behavior predicted by the linear elastic fracture mechanics. This strategy also enables the direct evaluation of the Stress Intensity Factors (SIFs) after a crack tip tying constraint is enforced at the crack tip to accommodate the additional enrichment parameters. Additionally, discontinuous functions are embedded into the displacement approximation of elements intercepted by cracks to avoid remeshing of these elements. For the discontinuous enrichment, new equations are provided by imposing displacement continuity conditions at the crack mouth. Shifted enrichment functions are used to preserve the physical meaning of the nodal parameters and to reduce the singularity order of the integral kernels containing the enrichment terms in the XBEM formulation. Furthermore, an enriched traction approximation is proposed to apply concentrated forces and support points along the boundary. When considering the XBEM formulation, changes in the conventional BEM are minimal, which facilitates the implementation of the extended approach into existing codes. Three numerical examples demonstrate the application of the proposed XBEM formulation in fracture modeling.