A Brief Review of Elasticity and Viscoelasticity for Solids (Advances in Applied Mathematics and Mechanics, 2011)
There are a number of interesting applications where modelingelastic and/or viscoelastic materials is fundamental, includinguses in civil engineering, the food industry, land mine detectionand ultrasonic imaging. Here we provide an overview of the subjectfor both elastic and viscoelastic materials in order to understandthe behavior of these materials. We begin with a briefintroduction of some basic terminology and relationships incontinuum mechanics, and a review of equations of motion in acontinuum in both Lagrangian and Eulerian forms. To complete theset of equations, we then proceed to present and discuss a numberof specific forms for the constitutive relationships between stressand strain proposed in the literature for both elastic andviscoelastic materials. In addition, we discuss someapplications for these constitutive equations. Finally, we give a computationalexample describing the motion of soil experiencing dynamicloading by incorporating a specific form of constitutive equationinto the equation of motion.