Dynamical extraction of a single chain from a discrete lattice

Abstract

We consider a nontrivial anti-plane shear fracture problem for a double-crack configuration where the remote external load is applied to the extracted mass-spring chain and the displacement field is symmetric with respect to the central axis between the cracks. An analytical solution obtained for the steady-state problem describes the displacement fields, stresses, local and global energy release rates and the dissipation. The double-crack configuration differs considerably from the classical problem of fracture in a lattice: the load is applied to the extracted chain rather than the outer domain as in the classical fracture problems. In the corresponding Wiener–Hopf equation, this leads to a special type of kernel, which is not typical for fracture problems.