Differentiation of energy functionals in two-dimensional elasticity theory for solids with curvilinear cracks. (Russian, English) Zbl 1087.74008

Rudoi, E. M.

J. Appl. Mech. Tech. Phys. 45, No. 6, 843-852 (2004); translation from Prikl. Mekh. Tekh. Fiz. 45, No. 6, 83-94 (2004).

The paper considers the equations of two-dimensional elasticity theory in nonsmooth domains with curvilinear cracks of variable length. On the crack faces, conditions are specified in the form of inequalities describing mutual nonpenetration of the crack faces. It is proved that the solutions of equilibrium problems with a perturbed crack converge to the solution of the equilibrium problem with an unperturbed crack in the corresponding function space. The author also obtains the derivative of the energy functional with respect to the length of the curvilinear crack.

Reviewer: N. I. Alexandrova (Novosibirsk)

MSC:

74B05	Classical linear elasticity
74R10	Brittle fracture
65K10	Numerical optimization and variational techniques

Keywords:

Griffith criterion; variational inequality; nonsmooth domain