Safe equilibrium and crack growth in inhomogeneous materials as a variational problem

Abstract: The variational principle of safe equilibrium for inhomogeneous elastic cracked bodies is formulated. Using the standard calculus of variations, we show that the crack remains in safe equilibrium as long as the maximum energy reduction rate of the virtually growing crack is negative. The crack starts to grow in the direction of the maximum energy reduction rate when the latter becomes zero. This energetic criterion implies the criteria proposed by He and Hutchinson (1989). As an application we use this criterion to predict the growth direction of an interface crack in a bimaterial.