Stress is the restoring force per unit area and strain is the fractional change in dimension. In general, there are three types of stresses (a) tensile stress – longitudinal stress (associated with stretching) or compressive stress (associated with compression), (b) shearing stress, and (c) hydraulic stress.
For small deformations, stress is directly proportional to the strain for many materials. This is known as Hooke’s law. The constant of proportionality is called modulus of elasticity. Three elastic moduli viz., Young’s modulus, shear modulus and bulk modulus are used to describe the elastic behaviour of objects as they respond to deforming forces that act on them. A class of solids called elastomers does not obey Hooke’s law.
When an object is under tension or compression, the Hooke’s law takes the form \( F / A=Y \Delta L / L \) where \(\Delta L / L\) is the tensile or compressive strain of the object, \(F\) is the magnitude of the applied force causing the strain, \(A\) is the cross-sectional area over which \(F\) is applied (perpendicular to \(A\) ) and \(Y\) is the Young’s modulus for the object. The stress is \(F / A\).
A pair of forces when applied parallel to the upper and lower faces, the solid deforms so that the upper face moves sideways with respect to the lower. The horizontal displacement \(\Delta L\) of the upper face is perpendicular to the vertical height \(L\). This type of deformation is called shear and the corresponding stress is the shearing stress. This type of stress is possible only in solids. In this kind of deformation the Hooke’s law takes the form \( F / A=G \times \Delta L / L \) where \(\Delta L\) is the displacement of one end of the object in the direction of the applied force \(F\), and \(G\) is the shear modulus.
When an object undergoes hydraulic compression due to stress exerted by a surrounding fluid, the Hooke’s law takes the form \( p=B(\Delta V / V) \) where \(p\) is the pressure (hydraulic stress) on the object due to the fluid, \(\Delta V / V\) (the volume strain) is the absolute fractional change in the object’s volume due to that pressure and \(B\) is the bulk modulus of the object.