Elasticity of Solids

Abstract

Abstract If a solid is initially at rest and equal and opposing forces are applied to that object, Newton’s Second Law guarantees that the object will remain at rest because the net force on the sample is zero. If that object is an elastic solid, then those forces will cause the solid to deform by an amount that is directly proportional to those applied forces. When the forces are removed, the sample will return to its original shape and size. That reversibility is the characteristic that is required if we say the behavior of the solid is “elastic.” This chapter will quantify the elastic behavior of solids by introducing the concepts of stress and strain and expressing their linear relationship through the definition of elastic moduli that depend only upon the material and the nature of the deformation and not upon the shape of the object. Those concepts allow us to generalize Hooke’s law. As before, the combination of a linear equation of state with Newton’s Second Law will now describe wave motion in solids. The introduction of a relaxation time, through the Maxwell model, will let these results be generalized to viscoelastic materials and then be applied to rubber vibration isolators.