| This paper deals with a novel approach, based on material differentiation of elastic BIE formulations, for the numerical computation of the energy release rate G along a crack front in 3-D elastic fracture problems. It is based upon the definition of G in terms of the material derivative of the potential energy at equilibrium W with respect to all possible regular virtual crack extensions. W can be formulated in terms of surface integrals; this fact in turn allows for a boundary-only formulation of its material derivative with respect to virtual crack extensions. The necessary step of computing the shape sensitivities of the boundary elastic variables is done by means of a derivative BIE. The latter results from a material differentiation of the primary elastic BIE, which is performed on a regularized (weakly singular) displacement BIE so that the process is mathematically sound. The unknowns of both primary and derivative BIEs are governed by the same integral operator, with obvious computational advantages. The present approach thus does not resort to any finite-difference evaluation of derivatives with respect to crack front perturbations. The implementation of the present method, including the key technical step of constructing appropriate vector interpolation functions for the transformation velocity associated with a virtual crack extension, is discussed. Finally, in order to demonstrate the potential of the proposed approach, numerical results are presented for two mode I examples where reference results are available for comparison: the round bar with a circular internal crack and the semielliptical surface crack, in both cases under uniform tension. |
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