Mathematical statement of elastodynamic contact problem for cracked body with considering unilateral restrictions and friction of the crack faces is done in classical and weak forms. Different variational formulations of unilateral contact problems with friction based on boundary variational principle are considered. Nonsmooth optimization algorithms of Udzawa’s type for solution of unilateral contact problem with friction have been developed. Convergence of the proposed algorithms has been studied numerically.

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A. N. Guz and V. V. Zozulya, “Elastodynamic Unilateral Contact Problems with Friction for Bodies with Cracks,” International Applied Mechanics, Vol. 38, No. 8, 2002, pp. 895-932.

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V. V. Zozulya and O. V. Menshykov, “Use of the Constrained Optimization Algorithms in Some Problems of Fracture Mechanics,” Optimization and Engineering, Vol. 4, No. 4, 2003, pp. 365-384.

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V. V. Zozulya, “Fracture Dynamics with Allowance for Crack Edge Contact Interaction,” In: C. Constanda, P. Schiavone and A. Mioduchowski, Integral Methods in Science and Engineering, Birkhauser, Boston, 2002, pp. 257-262.

V. V. Zozulya and P. Rivera, “Boundary Integral Equations and Problem of Existence in Contact Problems with Friction,” Journal of the Chinese Institute of Engineers, Vol. 3, No. 3, 2000, pp. 313-320.