Peridynamic Differential Operator

This chapter describes the construction of peridynamic (PD) functions and provides the PD form of local derivatives of up to second-order in 2D and 3D analyses. Also, it presents their analytical expressions for gradient, divergence, gradient of divergence, and the Laplacian of a displacement vector at a point with a complete horizon in the form of a sphere or a circle in accordance with the dimension of the analysis. Furthermore, it provides the PD form of the bond direction vector and its dyadic product with itself as well as the PD form of the divergence of a second-order tensor.