Nouvelle méthode semi-analytique pour exprimer les champs auxiliaires des intégrales d'intercations méthode de construction de champs auxiliaires

Abstract

The global approaches, such as the G-theta method, present the disadvantage of mixing the modes of fracture. This is necessary to differentiate for the application of kinking criteria (such as the “Principle of local symmetry”) in order to have the ability to numerically simulate the propagation of a three-dimensional crack. The extraction of the modes of fracture is carried out by the integral of interaction which exploits the bilinear term of the G-theta formulation applied to the superposition of two fields' solutions; the first field is the solution of the problem considered; the second field is the solution of a judiciously selected known problem. Its success depends on the validity of the auxiliary field (the second). As there are not analytical solutions for unspecified 3D cracks, it is usual to take as auxiliary fields the solutions of Westergard in each point of the crack face. We propose a new method of construction of these auxiliary fields (allowing to take into account the effects of a curved crack face) using integral representations.