II-Θ Method: a new method for the stability assessment of crack growth

Based on the continuum mechanics model, thereinafter is performed a mathematical formulation for the second derivatives of potential energy with respect to crack length in the framework of linear elasticity, in order to analyse the stability of a cracked system. We employ for this the perturbation domain technique with Lagrange coordinate; this leads to an explicit expression of the second derivatives which is particularly well amenable to the numerical computations. In the final section the second derivative is shown to be equal to a path independent integral termed D-integral