A modified peridynamics correspondence principle: Removal of zero-energy deformation and other implications

Abstract

We look for an enhancement of the correspondence model of peridynamics, emphasizing the elimination of zero-energy deformation modes. We propose an approach based on the notion of sub-horizons. The most useful feature of this proposal is the setup which, whilst providing solutions with the necessary stability, deviates only marginally from the original correspondence formulation. A thorough analysis of the sub-horizon based method is furnished based on the well-posedness of integral equations and energy spectrum, which clearly demonstrate a removal of zero energy modes. We also show how other forms of unphysical deformation modes, e.g. material collapse within horizon, jump discontinuities and vanishing energy modes, can be prevented with the present proposal. Finally, a set of numerical simulations are undertaken that attest to the remarkable efficacy of the sub-horizon based approach. © 2018 Elsevier B.V.