Viscoelastic material models in peridynamics

In this paper we propose a new viscoelastic material model within the framework of the nonlocal peridynamic formulation of continuum mechanics. Using Fourier- and Laplace-transforms we derive integral-representation formulas using a Green’s function approach for both local and nonlocal viscoelasticity. As an example we calculate the local and nonlocal response of an infinite viscoelastic bar impacted by a point load. We show both analytically and numerically that local viscoelasticity is recovered in the limit as the peridynamic lengthscales become small.