A variational technique for boundary element analysis of 3d fracture mechanics weight functions: dynamic

In this paper, a variational technique is described and used to determine the weight functions for three-dimensional dynamic, mixed-mode problems in fracture mechanics. The weight functions required to calculate the stress intensity factors are deÞned in terms of the derivatives of both traction and displacement for a reference problem. The solution of the simpler reference problem is obtained from a dual boundary element formulation in Laplace transform space. The stress intensity factors for any loading on the boundary in Laplace transform space can be calculated by a simple boundary integration when the transform parameter is Þxed. Then the stress intensity factors in the time domain are obtained by DurbinÕs inversion method. The accuracy of this technique for determining mixed-mode stress intensity factors is illustrated for a embedded circular slant crack, embedded elliptical crack and edge cracks in a rectangular bar suggested to either a uniform tensile load or a pure bending load on the ends of the bars