The application of peridynamics in predicting beam vibration and impact damage

A novel numerical method based on nonlocal peridynamic theory is applied to study the structural vibration and impact damage. Unlike Classical Continuum Mechanics (CCM) where conservation equations are cast into partial differential equations, peridynamics (PD) describes material behavior in terms of integro-differential equations, which may cope with discontinuous displacement fields commonly occurring in fracture mechanics. The main motivation of this paper is to validate the ability of 2D bond-based peridynamics in solving the material deformation in structural mechanics. The numerical results indicate that the peridynamic solutions for beams vibration problems are almost identical to the results based on classical Euler-Bernoulli beam theory. It is also found that the feature of “softer” material near the boundary in peridynamics has a notable effect on the solution of beam vibration. And the problem could be effectively solved by introducing a correction coefficient called “surface correction factor”. For the failure process of three-point bending beam with an offset notch, the simulation naturally captures the crack initiation and growth which is consistent with common failure mode observed in previous experimental investigations.