Elasticity is the property of a material to deform under the action of an imposed stress state (for example, due to external forces
applied) and then to reacquire its original form to the elimination of the urging cause. Elasticity applies to both solid materials and fluids.
The elasticity is explained, at the microscopic level, in the interaction forces that act between the particles that make up the material. The variation of these forces (due to external stress) changes the mutual distance between the particles (producing the deformation of the body at the macroscopic level). For relatively low levels of stresses, the necessary mechanical work is accumulated as mechanical energy within the material, and is released entirely when the stressing cause fails while the particles return to their initial position (the body acquires its original form).
Starting from the natural resting configuration, elasticity represents only the initial phase of the behavior of a material, for a limited value of the stress level. Each material has in fact a threshold of stresses, called the limit of elasticity, above which it ceases to exhibit an elastic behavior and shows inelastic phenomena (plasticity, rupture, etc.). In the case of ductile materials, the elastic limit is associated with the yield stress, in the case of fragile materials, the elastic limit is associated with the breaking of the material.
The simplest mathematical model of representation of elastic behavior is the linear model of Hooke's law (and of the generalized Hooke law in the case of multi-axial tension states). This model is of fundamental interest both in the theoretical field, for the possibility of being able to reach a complete mathematical study of the problems formulated, and in the engineering field, for the fall it has in the modeling and resolution of problems of technical and scientific interest. Other more complex mathematical models of nonlinear elasticity, important for the representation of the behavior of the tires, refer to the model of hyperelastic material, while for porous media the model declines in poroelasticity.