Defect nucleation modelling

The purpose of this article is to compare concepts of defect nucleation based on bifurcation of equilibrium solution and on damage modelling. The nucleation criterion is defined as a bifurcation of the equilibrium solutions of the perfect body and of the imperfect one when the size of the defect vanishes. The defect is considered as a small volume which evolves as a damaged zone. To study the influence of geometry of the defect on the critical loading governing its initiation, we consider the particular cases of a linear elastic composite sphere and of a linear elastic composite cylinder, for which the equilibrium solutions are known when the radial distribution of elastic bulk modulus is given simultaneously with a uniform shear modulus. The initial defect is a small sphere or a small cylinder, respectively, it can be a cavity or a kernel made with an elastic material with lower mechanical properties.