Figure 1

Descriptions of material point dynamics in continuum and discrete mechanics versus peridynamics. (a) Pictorial definition of internal stresses in continuum mechanics hypothesis. \({\mathbf{f}}_{int}\) is obtained by \(\operatorname{div}\boldsymbol{T}(\mathbf{x},t)\), where \(\boldsymbol{T}(\mathbf{x},t) \) is the stress tensor. (b) The material body is discretized by a network of edges connecting adjacent points. The summation of all local forces acting on x return the local value of \(\mathbf{f}_{int} \). (c) Within the peridynamics hypothesis, every point x is linked with all the points falling in its finite-range horizon, and \(\mathbf{f}_{int} \) is given by the integral of nonlocal forces acting on x