The dual boundary element formulation for elastoplastic fracture mechanics

Abstract

SUMMARYIn this paper the extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region fotmulation. In order to avoid collocation at crack tips, crack kinks and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elastoplastic behaviour is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This formulation was implemented for two-dimensional domains only, although there is no theoretical or numerical limitation to its application to three-dimensional ones. A centre-cracked plate and a slant edge-cracked plate subjected to tensile load are analysed and the results are compared with others available in the literature. J-type integrals are calculated.

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

“…for plain stress cases (4) where is Poisson's ratio. By differentiating Equation (1), rewritten for an internal point X in with respect to the co-ordinate of this point and applying the generalized Hooke's law to the elastic part of the total strain rate tensor, the following integral equation can be obtained for the stress rate at X :…”

“…During the past three decades, BEM has been successfully applied to elastoplastic contact analysis [2,3] and elastoplastic fracture analysis [4,5]. The boundary integral equations of elastoplastic problems include domain integrals, which can be evaluated by discretizing the nonlinear regions into internal cells.…”

Boundary element hyper-singular formulation for elastoplastic contact problems

“…Similar approaches can also be used for elastoplastic contact problems, for example see References [5][6][7].…”

Dual boundary element analysis for fatigue behavior of missile structures

“…For problems with a degenerate boundary, e.g., crack problems (Chen, 1988;Portela et al, 1992Portela et al, , 1993; Mi and Aliabadi, 1992; Fedelinski and Aliabadi, 1994; Leitao et al, 1995;Salgado and Aliabadi, 1998), flow around sheet piles (Chen and Hong, 1993;Chen et al, 1994), an incomplete partition in a room Chen and Wong, 1998) and a thin airfoil in aerodynamics (Wang et al, 1990;Chen and Hong, 1992), singularity exists, and the dual integral formulation has been applied successfully for the BEM approach. Using the dual integral formulation, all the well-posed boundary value problems can be solved even though a degenerate boundary is present.…”