Structural mechanics modeling of the impact of a double cantilever beam

A Global/Local model is developed for the calculation of dynamic stress intensity history resulting from the impact of a double cantilever beam. The model separates the Global structural dynamics from the Local crack tip zone dominated by singular stresses. The Global model, consisting of connected waveguides, describes the structural dynamics using spectral elements. The Local model, describing the crack tip behavior, is based on an application of the J-integral that converts the dynamic structural resultants directly into strain energy release rate. Previous work used this approach successfully for pure mode II deformation; the present paper extends the modeling to mode I and mixed mode deformation. Of special concern is the local modeling of the elasticity and mass in the vicinity of the crack tip; structural mechanics modeling is combined with Hamilton's principle to properly address this question. The accuracy of this approach is assessed by comparing it to a two dimensional finite element analysis.