2.1 INTRODUCTION

Two elastic constants of an elastic body are modulus of elasticity and Poisson's ratio. Modulus of elasticity is the ratio of normal stress to normal strain. It is generally denoted by the letter ‘E’. Units are gigapascal (GPa). The other elastic constant is Poisson's ratio.

Poisson's ratio is defi ned as the ratio of lateral strain to the longitudinal strain. It is denoted by the letter μ.

Consider a bar of length ‘L’ and diameter ‘d’ subjected to an axial tensile stress ‘σ’. ΔL is the longitudinal extension due to load P. Then, the longitudinal strain

Let Δd be the decrease in the lateral dimension of the bar.

The negative sign indicates that positive strain (increase) in longitudinal strain decreases the lateral dimension, thereby compressive strain in the lateral direction is induced.

Rigidity Modulus

Rigidity modulus is the ratio of shear stress to the corresponding shear strain. The unit is gigapascal. This is generally denoted by the letter ‘N’. The shear modulus or rigidity modulus appears in calculation where shape change occurs in the body.

Bulk Modulus

Bulk modulus is the ratio of direct stress or volumetric stress to the volumetric strain. It is denoted by the letter ‘K’ and unit is gigapascal. Generally in solids, the change in volume is very small, but this change in volume in case of fl uids will be considerable. Thus, bulk modulus appears in fl uid mechanics especially in compressible fl uid fl ow problems.

In the case of fl uids, stress at a point in all directions is same. Hence,

The bulk modulus and the rigidity modulus can be expressed in terms of modulus of elasticity and Poisson's ratio. Thus, the elastic constants for a homogeneous and isotropic body are two (2).

2.2 RELATIONSHIP BETWEEN E AND N

Consider a square block of unit width subjected to shear stress τ as shown in Figure 2.3. The shear stress τ induces vertical shear stress on planes AC and DB of same intensity ‘τ’. The shear stress on these planes is referred as complimentary shear stress.