Numerical Study of the Second-Order Peridynamic Material Correspondence Model

In this paper, a numerical study of the second-order model of recentlydeveloped higher-order peridynamic correspondence formulations is presented. Connectionsof the model with all three types of Mindlin first gradient theories areestablished. An implicit solution scheme based on the automatic differentiationtechnique for the construction of the stiffness matrix is developed. To examinethe material stability of the model, a wave dispersion analysis is conducted fordifferent combinations of horizon size and length scale parameter. To verify theprediction accuracy of the model, a benchmark linear elastic deformation problemwith analytical solution is modeled for different length scale parameters. From thewave dispersion analysis, it is found that the second-order model is stable as longas the material has nonzero length scale parameter. It is also found that increasingthe size of either the mesh spacing factor or the length scale parameter reducesthe dispersiveness of the angular frequency - wave number curve while increasingmesh spacing increases the dispersiveness of the curve. In the linear elastic deformationstudy, great agreements between the model predictions and the analyticalsolutions for nonzero length scale parameters are observed. For small length scaleparameter, both the model prediction and the analytical solution are very closeto conventional solution without considering length scale effect. This observationverifies the prediction accuracy of the model and confirms the ability of the modelto accurately capture the length scale effect in materials.