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A Brief Review of Elasticity and Viscoelasticity for Solids

A Brief Review of Elasticity and Viscoelasticity for Solids
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Year:    2011

Author:    Harvey Thomas Banks, Shuhua Hu, Zackary R. Kenz

Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 1 : pp. 1–51

Abstract

There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m1030

Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 1 : pp. 1–51

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    51

Keywords:    Mathematical modeling Eulerian and Lagrangian formulations in continuum mechanics elasticity viscoelasticity computational simulations in soil constitutive relationships. continuum mechanics Bombyx mori silk fibroin Nonlinear wave equation

Author Details

Harvey Thomas Banks

Shuhua Hu

Zackary R. Kenz

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