STEADY-STATE SOLUTIONS FOR A VISCOELASTIC CRACK UNDER AN ALTERNATING BENDING MOMENT

The solution of the problem of a crack in a viscoelastic medium subjected to a sinusoidal bending moment is formulated in terms of non-singular integral equations in space and time. These are solved numerically in the steady-state limit. The partial closing of the crack is smooth, though generally rapid, rather than sudden, in contrast to the behaviour of an elastic medium. An approximate method of solution, much simpler than the exact method, is also proposed. The integral equation method used to solve this problem is one of considerable generality. It was previously used to solve problems with transversely moving indentors on viscoelastic media. Potentially, it can be adapted to solve any non-inertial viscoelastic boundary value problem that cannot be treated by easier techniques. However, it will generally be the case that numerical methods must be used to solve the integral equations.