Math Solution of Elasticity

When an elastic material is deformed due to an external force, it experiences internal forces that oppose the deformation and restore it to its original state if the external force is no longer applied. There are various elastic moduli, such as Young’s modulus, the shear modulus, and the bulk modulus, all of which are measures of the inherent stiffness of a material as a resistance to deformation under an applied load. The various moduli apply to different kinds of deformation. For instance, Young’s modulus applies to uniform extension, whereas the shear modulus applies to shearing.