ON THE MODELING OF THE CONTACT INTERACTION IN THE MECHANICS OF QUASI-BRITTLE FRACTURE

The loading of an elastic body with an initial crack is considered. In analyzing the development of the crack during the process of loading, one should take into account the possibility of contact of the surfaces of the crack. This leads to the complex boundary-value problems with unknown boundaries delined by closing and opening of the surfaces of the crack. The difficulties caused by unknown boundaries are characteristic of the problems with unilateral constraints. To overcome these difficulties, an approach is suggested which is based on filling the clearance between the surfaces of the crack with an artificial material. The moduli of stiffness of this material are much less than the corresponding moduli of the material of the body. The problems thus modified can be solved using familiar algorithms and available software for the modified problems of loading of a piecewise-homogeneous medium. The solutions obtained on the basis of the approach suggested are presented. The errors are estimated depending on the properties of the artificial material.