Shape sensitivity analysis for energy release rate evaluation and its application to the study of three-dimensional cracked bodies

The energy release rate is an important parameter for the analysis of crack ed bodies in linear elastic fracture mechanics. This parameter, usually den oted by G, is equivalent to Pi, the rate of change with respect to crack ch ange of the energy available for fracture. In this paper, crack growth is s imulated by an action of change of the shape of the body characterized by a n appropriate known smooth velocity field v defined over the domain of the body. A general (integral) expression for Pi using shape sensitivity analys is based on distributed parameters is also obtained in this paper. Since th is expression depends on the displacement field u and on del v, a simple po st-processing technique is required for the: numerical evaluation of this e xpression. An adaptive finite element analysis is performed in order to ens ure a good accuracy during the numerical evaluation of Pi. Finally, well kn own three-dimensional examples in fracture mechanics are considered in orde r to illustrate the potentiality of the proposed methodology. (C) 2000 Else vier Science S.A. All rights reserved.