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A Brief Review of Elasticity and Viscoelasticity for Solids

Published online by Cambridge University Press:  03 June 2015

Harvey Thomas Banks ,
Shuhua Hu  and
Zackary R. Kenz
Harvey Thomas Banks*
Affiliation:
Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8212, USA
Shuhua Hu*
Affiliation:
Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8212, USA
Zackary R. Kenz*
Affiliation:
Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8212, USA
*
Corresponding author. URL: http://www.ncsu.edu/crsc/htbanks/ Email: htbanks@ncsu.edu
Email: shu3@ncsu.edu
Email: zrkenz@ncsu.edu

Abstract

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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.

Keywords

93A3074B0574B2074D0574D10Mathematical modelingEulerian and Lagrangian formulations in continuum mechanicselasticityviscoelasticitycomputational simulations in soilconstitutive relationships
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 1 , February 2011 , pp. 1 - 51
Copyright
Copyright © Global-Science Press 2011

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