What is linear elasticity ?

Hint:We know that elasticity is the property of an object to retain back its original dimensions when it is stretched(strain) or compressed(stress). Linear describes the nature of the relationship between two quantities.

Complete answer:
In basic mechanics, a spring's elasticity is expressed by Hooke's law, which states that force required to stretch or compress spring is proportional to how much the spring is stretched or compressed. The result of Hooke's law is that stress is proportional to strain in continuous elastic materials. Some materials that we consider to be highly elastic, such as rubber, do not follow Hooke's law unless they are subjected to very small deformations.

As stresses become too great, most materials deform more than Hooke's law predicts. When objects follow the Hooke’s law and the relationship between the stress and strain on the object is linear. Elasticity of an object when it is assumed to follow the Hooke’s law is known as linear elasticity. Moreover, linear elasticity is a mathematical term that describes how solid objects deform when force is applied on them.

This study is a branch of continuum mechanics and is a simplification of the general non-linear theory of elasticity in several ways. The fundamental assumptions of linear elasticity model are:
(i) Infinitesimal strains or small deformations (or strains) and
(ii)Linear relationships between the components of stress and strain.
(iii) valid only if the stress states do not produce yielding.

Note: As loads are applied to rigid structures, linear elasticity defines how they bend and become internally stressed. For several engineering materials and engineering design situations, the assumptions of linear elasticity are rational. As a result, linear elasticity is widely used in structural analysis and engineering design, often in conjunction with finite element analysis.