Modeling material length-scale effect using the second-order peridynamic material correspondence model

In this paper, a study on modeling material length-scale effect using peridynamics via the second-order material correspondence formulation is presented. Connections of the second-order model with all three types of Mindlin first gradient theory are established. An implicit solution scheme based on the automatic differentiation technique for the construction of the stiffness matrix for linear elastic problems is developed. Numerical examples are used to examine the material stability of the model and verify its capability in modeling material length-scale effect for different length-scale parameters. From the wave dispersion analysis, it is found that the second-order model is stable as long as the material has nonzero length-scale parameter. In the linear elastic deformation study, great agreements between the model predictions and the analytical solutions for nonzero length-scale parameters are observed.