ELASTIC BEHAVIOR OF MATERIALS

Let us study about elastic behavior of materials,
When a real material is studied at progressively diminishing scales, it is usually found to exhibit a
variation in properties from point to point. This variation is called structure. The term is often used with reference to a certain scale, e.g., atomic structure, microstructure, etc. The mechanical response of material to loading depends on its structure, and a large section of materials science is devoted to the analysis of this dependence. However, some fundamental aspects of mechanical behavior can be understood very well if the material is considered to be structureless,
a solid continuum. Solids respond to applied external loads by developing internal forces. If an imaginary section through the solid is considered, the components of internal force acting on a unit elemental area are called stresses.

Under the action of stresses solids deform, so that the distances between points change. However, provided the stresses are sufficiently small, the solid recovers its original shape and volume once the load is removed. This type of behavior is called elastic. Continuum elasticity considers the consequence of atomic interactions in solids, but disregards their nature. The
atomic aspects of elastic deformation are considered in Elastic BehaŠior of Materials: Physical Basis. Nonelastic behavior is manifested in residual deformation persisting after load removal, and often gives rise to residual stress. Under very low loads, deformation is found to be proportional to stress. The case of linear continuum elasticity is the main subject of this article. First, the foundations of stress and strain are laid out in the infinitesimal limit. Then simple forms of the elastic equations for isotropic bodies are introduced using
Lame!'s constants, as well as Young's modulus and Poisson's ratio.
Hope the above explanation helped you.