Elasticity (physics)

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Continuum mechanics

General

Classical mechanics Stress / Strain Tensor Conservation of mass Conservation of momentum

Solid mechanics

Solids Elasticity Plasticity Hooke's law Poisson's ratio Rheology

Fluid mechanics

Fluids Fluid statics Fluid dynamics Navier-Stokes equations Viscosity Newtonian fluids Non-Newtonian fluids

Elasticity is a branch of physics which studies the properties of elastic materials. A material is said to be elastic if it deforms under stress (e.g., external forces), but then returns to its original shape when the stress is removed. The amount of deformation is called the strain.

Contents 1 Modeling elasticity 2 Transitions to inelasticity 3 See also 4 References

[edit] Modeling elasticity

Under small stresses many solids' strains are roughly proportional to the stresses they are undergoing. The constant of proportionality (sometimes known as the elasticity), is given by the reciprocal of Young's modulus of elasticity, which is a measure of stiffness. Thus, elasticity is typically modeled using a linear relationship between stresses and strain (see "Linear elasticity"). The classic theoretical example of linear elasticity is the perfect spring, whose behavior is described by Hooke's law. Linear elasticity, however, is an approximation; real materials exhibit some degree of non-linear behavior. Whether working with linear or non-linear models, the relationship between stress and strain is often described using tensor methods and the elasticity tensor.

[edit] Transitions to inelasticity

Above a certain stress known as the elastic limit or the yield strength of an elastic material, the relationship between stress and strain breaks down. Beyond this limit, the solid may deform irreversibly, exhibiting plasticity. This phenomenon is often observed using stress-strain curves.

Furthermore, not only solids exhibit elasticity. Some non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions. 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, exhibiting viscosity.

[edit] See also

• Stiffness
• Elastic modulus
• Linear elasticity
• 3-D Elasticity
• Pseudoelasticity

[edit] References

• L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics: Theory of Elasticity Butterworth-Heinemann, ISBN 0-7506-2633-X
• J.E. Marsden, T.J. Hughes, Mathematical Foundations of Elasticity, Dover, ISBN 0-486-67865-2
• P.C. Chou, N. J. Pagano, Elasticity: Tensor, Dyadic, and Engineering Approaches, Dover, ISBN 0-486-66958-0
• R.W. Ogden, Non-linear Elastic Deformation, Dover, ISBN 0-486-69648-0