Dispersive Wave Propagation in the Nonlocal Peridynamic Theory

Peridynamics is a nonlocal formulation of continuum mechanics that is oriented toward deformations including discontinuities, especially fractures. However already the linear elastic problem is considerably more complex than the corresponding local problem governed by the NAVIER equations. For example, the presence of long-range forces leads to the dispersion of elastic waves. The amount of dispersion is governed by the peridynamic horizon, a length-scale that naturally appears in in the equation of motion. Another example is the emergence and propagation of discontinuities that can be observed by studying the RIEMANN problem. In this presentation we show how FOURIER transformations can be used to find a representation of the solution of the general inhomogeneous initial value problem for the 3D linear bond-based peridynamic formulation. Several examples illustrate this approach and show the importance of the peridynamic horizon. Finally we demonstrate how the nonlinear dispersion relation can be used to capture experimentally measure dispersion relations.