Dynamic interfacial fracture with higher-order vibration modes

The dynamic energy release rate (ERR) of a stationary crack in a double cantilever beam (DCB) under a constant applied opening rate at the free end is derived using beam dynamics, and completely analytical formulae are obtained. It is discovered that the dispersive propagation of flexural waves must be considered otherwise the contributions to the dynamic ERR from the higher-order vibration modes cannot be correctly captured. In addition, it is shown that the intact part of the DCB (ahead of the crack tip) can be replaced with a single vertical spring and a rotation constraint at the crack tip to significantly simplify the analytical modeling. The dynamic ERR is accurately captured in comparison to finite element method (FEM) simulations, including the higher-order vibration modes.