EXTENSIONS OF THE PSEUDO TRACTIONS TECHNIQUE FOR FRICTION IN CRACKS, CIRCULAR CAVITIES AND EXTERNAL BOUNDARIES - EFFECT OF THE INTERACTIONSON THE HOMOGENIZED STIFFNESS

This paper deals with interactions in a two-dimensional cracked and po rous medium. Interactions are computed using a semi analytical method based on 'pseudo tractions', in order to quantify the global behaviour of cracked materials. The number of singularities induced by cracks s hows that the analytical pseudo tractions based on linear elastic frac ture mechanics can be used to solve problems involving interactions. I t is explained how the original technique of computation of interactio ns between cracks can be extended to finite media containing both circ ular cavities and cracks, with a Coulomb model for friction in cracks. The ability of the method to give accurate results is illustrated wit h some examples. The effects of interactions and presence of boundarie s, introduced at a mesoscale, are illustrated here by some examples co nsidering the global stiffness of the cracked media under tensile load ing. The necessity of the computation of the interactions is related t o the density of the cracks. Some simple expressions available in the cases of weak interactions, and allowing friction in cracks, are devel oped. The pseudo tractions results are compared to those given by self consistent and differential techniques. Results involving porosity an d crack closure with friction were shown in a previous paper [7].