Effect of the contact of crack lips under variable loads

We formulate a contact problem of the theory of elasticity with unilateral constraints for cracked bodies under random variable loading and consider a special case of harmonic loads very important for practical applications. The problem is solved by the method of boundary integral equations of the elastodynamic theory of cracked bodies, We also analyze typical singularities of the kernels of potentials of these equations and develop an algorithm for the solution of unilateral contact problems of the dynamics of cracked bodies based on the determination of the saddle point of a subdifferential boundary functional. We solve dynamical problems of propagation of plane harmonic compression-dilatation waves in a plane with cracks of finite lengths under the assumption of unilateral contact of the crack lips. We present numerical results and investigate the effect of contact interaction of the crack lips both quantitatively and qualitatively.