@Article{AAMM-3-1,
author = {Banks , Harvey ThomasHu , Shuhua and Kenz , Zackary R.},
title = {A Brief Review of Elasticity and Viscoelasticity for Solids},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2011},
volume = {3},
number = {1},
pages = {1--51},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m1030},
url = {http://global-sci.org/intro/article_detail/aamm/155.html}
}