Elastic Constants

As there are different kinds of stresses possible, such like linear (normal) stress, volumetric (bulk) stress,  shear stress, and correspondingly different modulii of elasticity namely, shear modulus, Young's modulus and bulk modulus are described as elastic constants of a material. The term E is utilized in Eqs. (1) and (2) in the context of normal stresses and equivalent strains is called as Young's Modulus.

Additionally to the three modulii of elasticity a significant elastic constant, utilized in defining the mechanical properties of a solid, is called as Poisson's ratio. While testing the material for stress-strain relationship, you observe that strains are generated not only in the direction of the applied stress, but also in direction perpendicular (lateral) to it. On further investigations, you shall discover that the lateral strain is always proportional to the longitudinal strain and the proportionality constant is negative. This proportionality constant is explained as Poisson's Ratio and mentioned by υ.

 ∴ Poisson's Ratio, υ =- Lateral Strain/ Longitudinal Strain

When applying tensile force on a rod we found that the deformations generated involved change of volume of the solid with its shape. Such deformations might be found in many other cases of loading. Deformations including modification of volume & shape are more common. Though, we might identify two special cases of deformations that is dilatation, & distortion.