Numerical Methods for the Nonlocal Wave Equation of the Peridynamics
For engineers modeling mechanical systems with peridynamics, this work offers improved computational methods, but the contribution is incremental as it extends existing techniques to a specific domain.
This paper reviews and proposes new higher-order numerical methods for solving the nonlocal wave equation in peridynamics, demonstrating their effectiveness through numerical tests.
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering because seems to provide an effective approach to modeling mechanical systems avoiding spatial discontinuous derivatives and body singularities. In particular, we will consider the linear model of peridynamics in a one-dimensional spatial domain. Here we will review some numerical techniques to solve this equation and propose some new computational methods of higher order in space; moreover we will see how to apply the methods studied for the linear model to the nonlinear one. Also a spectral method for the spatial discretization of the linear problem will be discussed. Several numerical tests will be given in order to validate our results.