The sensitivities of fracture parameters in cracked structures provide useful information for the prediction of stability and arrest of a single crack, the growth pattern analysis of a system of interacting cracks, configurational stability analysis of evolving cracks, probabilistic fracture mechanics analysis and universal size effect model. In the case of multiple crack systems, for example, sensitivities of fracture parameters at one crack tip due to the growth of any other crack must be calculated to determine the strength of the interaction. In probabilistic fracture mechanics analysis of linear-elastic cracked structures, the first and second order reliability methods require accurate estimates of fracture parameters, their sensitivities. This paper presents a new fractal finite element method based continuum shape sensitivity analysis for evaluating sensitivities of fracture parameters in a homogeneous, isotropic, and two dimensional linear-elastic multiple cracked system subject to mixed-mode loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of fracture parameters. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predict the first-order sensitivity of fracture parameters, more efficiently and accurately than the finite-difference method.
Elastic-plastic fracture mechanics analysis by combination of boundary element and finite element methods.