Variational formulation and nonsmooth optimization algorithms in elastodynamic contact problems for cracked body

A mathematical model of an elastodynamic contact problem for a body with a crack with unilateral restrictions and friction on the crack faces is presented in classical and weak forms. Different variational formulations of unilateral contact problems with friction based on the principles of Hamilton–Ostrogradskii and Tupin, and boundary variational principles are considered. In particular, boundary variational functionals that are used with boundary integral equations are established. Nonsmooth optimization algorithms of Udzawa type for the solution of these unilateral contact problems with friction are developed. The convergence of the proposed algorithms is studied numerically.