Shape sensitivity analysis in linear elastic fracture mechanics

Abstract

Shape sensitivity analysis of an elastic solid in equilibrium with a known load system applied over its boundary is presented in this work. The domain and boundary integral expressions of the first- and second-order shape derivatives of the total potential energy are established, by using an arbitrary change of the domain characterized by a velocity field defined over the initial body configuration. In these expressions we recognize free divergence tensors that are denoted in this paper as energy shape change tensors. Next, shape sensitivity analysis is applied to cracked bodies. For that purpose, a suitable velocity distribution field is adopted to simulate the crack advance of a unit length in a two-dimensional body. Finally, the corresponding domain and the equivalent path-independent integral expressions of the first- and second-order potential energy release rate of fracture mechanics are also derived.