# Viscoelastic material models in peridynamics

Olaf Weckner, Nik Abdullah Nik Mohamed

Research output: Contribution to journalArticle

23 Citations (Scopus)

### Abstract

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.

Original language English 6039-6043 5 Applied Mathematics and Computation 219 11 https://doi.org/10.1016/j.amc.2012.11.090 Published - 2013

### Fingerprint

Viscoelastic Material
Viscoelasticity
Continuum mechanics
Laplace transforms
Green's function
Fourier transforms
Representation Formula
Continuum Mechanics
Integral Formula
Integral Representation
Length Scale
Laplace transform
Fourier transform
Model
Calculate
Formulation

### Keywords

• Nonlocality
• Peridynamics

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics

### Cite this

Viscoelastic material models in peridynamics. / Weckner, Olaf; Nik Mohamed, Nik Abdullah.

In: Applied Mathematics and Computation, Vol. 219, No. 11, 2013, p. 6039-6043.

Research output: Contribution to journalArticle

Weckner, Olaf ; Nik Mohamed, Nik Abdullah. / Viscoelastic material models in peridynamics. In: Applied Mathematics and Computation. 2013 ; Vol. 219, No. 11. pp. 6039-6043.
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