Abstract
The dynamic problems of fracture mechanics for composite materials with initial stresses are considered in the case of cracks moving at a constant rate along a straight line. In the continuum approximation, composite materials are modeled by orthotropic nonlinearly elastic bodies with an arbitrary form of the elastic potential. A three-dimensional linearized theory of elasticity is used. The complex potentials of plane and antiplane problems of the linearized theory are used for dynamic problems. Exact solutions for Modes I, II, and III in the case of moving cracks are obtained using the Keldysh-Sedov methods. Asymptotic formulas for stresses and displacements near the crack tip for Modes I, II, and III are presented. The basic mechanical effects are analyzed with respect to the problems considered.
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