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

Abstract

The energy release rate is an important parameter for the analysis of cracked bodies in linear elastic fracture mechanics. This parameter, usually denoted by G, is equivalent to Π ̇ , the rate of change with respect to crack change of the energy available for fracture. In this paper, crack growth is simulated by an action of change of the shape of the body characterized by an appropriate known smooth velocity field v defined over the domain of the body. A general (integral) expression for Π ̇ using shape sensitivity analysis based on distributed parameters is also obtained in this paper. Since this expression depends on the displacement field u and on ∇ v , a simple post-processing technique is required for the numerical evaluation of this expression. An adaptive finite element analysis is performed in order to ensure a good accuracy during the numerical evaluation of Π ̇ . Finally, well known three-dimensional examples in fracture mechanics are considered in order to illustrate the potentiality of the proposed methodology.