STRONG DISPLACEMENT DISCONTINUITIES AND LAGRANGE MULTIPLIERS: FINITE DISPLACEMENT FORMULATION IN THE ANALYSIS OF FRACTURE PROBLEMS

Abstract

IN THIS WORK, THE IMPLICIT BEM FORMULATION, INITIALLY DEVELOPED IN THE CONTEXT OF PLASTICITY ANALYSIS IS EXTENDED TO INCORPORATE DAMAGE MECHANICS MODELS. THE ALGEBRAIC EQUATIONS ADOPTED FOR THE FORMULATION ARE OBTAINED EITHER USING DISPLACEMENT OR TRACTION REPRESENTATIONS, FOR BOUNDARY NODES, AND STRESS EQUATIONS FOR INTERNAL NODES. THE FORMULATION IS MODI¯ED TO INCORPORATE THE REGULARIZATION TECHNIQUE BASED ON THE NON-LOCAL INTEGRAL. THE CONSISTENT TANGENT OPERATOR HAS BEEN OBTAINED FOR LOCAL AND NON-LOCAL FORMULATIONS. THE ARCLENGTH CONCEPT DEVELOPED FOR BEM FORMULATIONS IS ADOPTED TO ANALYSE PROBLEMS EXHIBITING THE SNAP-BACK EFFECTS.