Dynamic delamination on elastic interface

•Analytical theory for dynamic energy release rate of a double cantilever beam.•Consideration of dynamics, including vibration, and dispersive wave propagation.•Dynamic factor due to vibration quantifies contribution from each vibration mode.•Finite-element-method simulations verify the analytical theory with good agreement. The dynamic energy release rate (ERR) is derived for a delamination on the interface between a partially supported vibrating beam and an elastic foundation, with a time-dependent displacement applied to the beam’s free end. The configuration may represent, for example, the dynamic delamination of a laminated composite, or the cracking of a typical adhesively bonded composite joint. The developed theory is completely analytical and applicable to both symmetric double cantilever beams (DCBs) and thin layers on thick substrates. It was discovered that the dispersive propagation of flexural waves should be considered in order to capture contributions to the ERR from higher-order vibration modes. The developed theory is verified using finite-element-method (FEM) simulations and they are found to be in excellent agreement. This work will be useful to characterize the dynamic fracture toughness of layered materials in DCB tests, and to determine the fracture behavior of engineering structures under dynamic loads. Furthermore, the partially supported beam’s elastic foundation is relevant for the study of crack process zones, which are usually analyzed using the FEM and the cohesive-zone model. The potential applications of this study include determining the dynamic fracture toughness for crack initiation in laminated composite DCBs and adhesively bonded structures.