The Micro-Bond Potential and Stress Tensor in Peridynamics Revisited

The micro-bond potential and stress tensor in Peridynamics are examined. A new form of the 3D micro-bond potential is proposed in terms of the components of the bond length change. The present micro-bond potential provides a new route to unifying the classical 3D bond-based and ordinary state-based Peridynamics, and it also appears to be central to developing potential-based bond failure criteria, especially for the ordinary state-based Peridynamics. Besides, a new measure of Peridynamic stress is introduced. Different from the available Peridynamic stress tensors, the present Peridynamic stress is derived from the deformation state in a direct way and equivalent to the Cauchy stress to some extent. Moreover, the Peridynamic partial stress is critically reexamined. Straightforward proof shows the exact relationships among the Peridynamic partial stress, the present Peridynamic stress and the first Piola stress.