Weight functions in two-dimensional bodies with arbitrary anisotropy

Computation of shear mode weight functions for circular and elliptical cracks

“…"Cvz ,. * "r*xy ) = 0(p-3/2), (1) where O is the order symbol. The geometric intensity coefficients of the ordinary fundamental field are defined through the displacement field on C + as [7] x~u* --+ m*, x/pv* -'+ -m*,, xfpw* --+ m* (2) as p--+0.…”

“…The internal surface separating region B from the rest of the body is denoted as Sin t and this internal surface does not include the crack face. This finite element procedure has been used to determine two-dimensional weight functions in isotropic [4], anisotropic [1] and layered [3] solids as well as three-dimensional mode I weight functions [6]. In the finite element implementation, the displacements W ~ or W~ at the nodal points and the corresponding stresses at the Gauss points on the surface Sint as generated by the shear mode potentials through (11) and (12) are needed.…”

“…Recent papers, [1,2,3], have shown that the finite element procedure based on the variational principle introduced by Sham [4] is very efficient for determining the fundamental fields directly for two-dimensional crack problems in both isotropic and anisotropic solids under either traction or mixed boundary conditions for all three fracture modes. It can also be used in calculating high order weight functions for linear elastic plane problems [5].…”

Analytical solution for orthotropic composite plate containing a mode I crack along principle axis

“…The stress distribution at the crack tip of orthotropic materials was numerically analyzed by Wang et al [10]. In the last two decades, much research has been addressed to the calculation of the stress intensity factor for composite materials by the theoretical method [11][12][13] and numerical methods including finite element method [14][15][16][17][18], boundary element method [19], Green function [20], variational approximation method [21][22] and weight function method ] [23][24][25]. However, a knowledge of the stress and displacement fields around the tip is the key to expressing the fracture strength of a cracked composite material.…”

Analysis of an internal crack in a finite anisotropic plate

“…For example, Wang et al [12] solved the mixed mode crack problem by Finite Element Method based on the conservation laws of anisotropic elasticity. Deukman An [13], Sham and Zhou [14] also developed a FEM procedure with weight functions to determine the two-dimensional fundamental fields in anisotropic solids. On the other hand, Boundary Collocation Method (BCM) has been shown as an effective method for a variety of crack problems for plates of finite geometry with isotropic and homogeneous materials [15][16][17][18][19][20][21][22][23][24].…”