Volume 3, Issue 1
A Brief Review of Elasticity and Viscoelasticity for Solids

Adv. Appl. Math. Mech., 3 (2011), pp. 1-51.

Published online: 2011-03

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• 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.

93A30, 74B05, 74B20, 74D05, 74D10

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@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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1030}, url = {http://global-sci.org/intro/article_detail/aamm/155.html} }
TY - JOUR T1 - A Brief Review of Elasticity and Viscoelasticity for Solids AU - Banks , Harvey Thomas AU - Hu , Shuhua AU - Kenz , Zackary R. JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 1 EP - 51 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1030 UR - https://global-sci.org/intro/article_detail/aamm/155.html KW - Mathematical modeling, Eulerian and Lagrangian formulations in continuum mechanics, elasticity, viscoelasticity, computational simulations in soil, constitutive relationships. AB -

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.

Harvey Thomas Banks, Shuhua Hu & Zackary R. Kenz. (1970). A Brief Review of Elasticity and Viscoelasticity for Solids. Advances in Applied Mathematics and Mechanics. 3 (1). 1-51. doi:10.4208/aamm.10-m1030
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