# Theory of elasticity

The study of the physics of continuous materials which deform when subjected to a force. Overview[ edit ] When an elastic material is deformed due to an external force, it experiences internal resistance to the deformation and restores it to its original state if the external force is no longer applied. There are various elastic modulisuch as Young's modulusthe shear modulusand the bulk modulusall of which are measures of the inherent elastic properties of a material as a resistance to deformation under an applied load. The various moduli apply to different kinds of deformation. If the material is isotropicthe linearized stress—strain relationship is called Hooke's lawwhich is often presumed to apply up to the elastic limit for most metals or crystalline materials whereas nonlinear elasticity is generally required to model large deformations of rubbery materials even in the elastic range.

For even higher stresses, materials exhibit plastic behaviorthat is, they deform irreversibly and do not return to their original shape after stress is no longer applied. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape.

Under larger strains, or strains applied for longer periods of time, these fluids may start to flow like a viscous liquid. Because the elasticity of a material is described in terms of a stress—strain relation, it is essential that the terms stress and strain be defined without ambiguity.

Typically, two types of relation are considered. The first type deals with materials that are elastic only for small strains. The second deals with materials that are not limited to small strains.

Clearly, the second type of relation is more general in the sense that it must include the first type as a special case. For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor ; the resulting predicted material behavior is termed linear elasticitywhich for isotropic media is called the generalized Hooke's law.

Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for the possibility of large rotations, large distortions, and intrinsic or induced anisotropy. For more general situations, any of a number of stress measures can be used, and it generally desired but not required that the elastic stress—strain relation be phrased in terms of a finite strain measure that is work conjugate to the selected stress measure, i.

Linear elasticity As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain. This relationship is known as Hooke's law.

A geometry-dependent version of the idea  was first formulated by Robert Hooke in as a Latin anagram"ceiiinosssttuv". He published the answer in This law can be stated as a relationship between tensile force F and corresponding extension displacement x, F.Normally, textbooks in elasticity after Timoshenko commonly used his solutions and formulations.

Timoskenko's other classic books on Theory of Elastic Stability and Theory of Elastic Plates and Shells are also highly recommended if you are doing specific elastic members attheheels.coms: A comprehensive textbook covering not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subject, such as thermal conduction and viscosity in solids.

Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Elasticity, Theory of the branch of mechanics that studies the displacements, strains, and stresses that occur under the action of loads in elastic bodies at rest or in motion.

The theory of elasticity is the basis for calculations of strength, deformability, and stability in construction, aircraft and rocket building, machine building, mining, and.

L.D. Landau & E.M. Lifshitz Theory of Elasticity (Volume 7 of A Course of Theoretical Physics) Pergamon Press Acrobat 7 Pdf Mb. Theory of Elasticity The property of solid materials to deform under the application of an external force and to regain their original shape after the force is removed is referred to as its elasticity.

Linear elasticity - Wikipedia