A mode III rate-dependent bridged crack with surface elasticity

A mode III rate-dependent bridged crack with surface elasticity is studied. The surface elasticity on the crack faces is incorporated by using a version of the continuum-based surface/interface theory of Gurtin and Murdoch. The bridging force along the crack is proportional, in terms of the constant or variable bridging viscosity, to the time-rate of the crack opening displacement. The Green's function method is used to derive a complete and transient solution by reducing the boundary value problem to a Cauchy singular integro-differential equation which can be further changed into state-space equations by means of the collocation method. The state-space equations are solved by a rigorous analysis of the eigenmodes. Detailed numerical results are presented for eigenvalues, eigenfunctions, and the evolution of the bridging force, crack opening displacement and the strength of the logarithmic singularity at the crack tips.