Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress (average internal repair force per unit area) and strain (relative strain). Under small deformation, most elastic materials (such as springs) exhibit linear elasticity, can be described by the linear relationship between stress and strain, and follow Hooke’s law. Hooke's law states that the force required to deform an elastic object is directly proportional to the distance of the deformation. The elastic limit or yield point of a material refers to the maximum stress that the material can bear before the deformation is permanent (plastic deformation). For example, in a spring, stress is proportional to strain, and the elastic modulus of the material is the proportional constant related to stress and strain.
This text is adapted from Openstax, University Physics Volume 1, Section 12.4: Elasticity and Plasticity.