The Peridynamic Material Correspondence Models: A State-of-the-Art Review on Stabilization Schemes

This paper reviews the peridynamic material correspondence models and discusses how the material instability or zero-energy modes in the conventional model is handled in each of these models. The material correspondence formulation enables direct incorporation of material constitutive models from the local continuum theory for peridynamics. However, the well-known issue of material instability or zero-energy modes in the material correspondence formulation has prevented its broad applications. To stabilize the conventional formulation, various numerical techniques have been developed in the literature, including the supplemental force method, modified strain measurement method, field averaging method, stress point method, and bond-associated method. Among these methods, the bond-associated method is particularly promising due to its free of additional terms and calibrated control parameters. The effectiveness of five representative material correspondence models in removing zero-energy modes is tested via wave dispersion analysis.