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Elasticity (physics)
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, elasticity is the physical property
Physical property

A physical property is any aspect of an object or substance that can be measurement or perception without changing its Identity . Physical properties can be Intensive and extensive properties....
 of a material when it deforms under stress
Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
 (e.g. external force
Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
s), but returns to its original shape when the stress is removed. The amount of deformation
Deformation

In materials science, deformation is a change in the shape or size of an object due to an applied force . This can be a result of tensile strength forces, compressive strength forces, Simple shear, bending or torsion ....
 is called the strain
Strain

Strain can refer to:* Strain , a variant of a plant, virus or bacterium; or an inbred animal used for experimental purposes* Strain , a chemical stress of a molecule...
.

Modeling elasticity
The elastic regime is characterized by a linear relationship between stress and strain, denoted linear elasticity
Linear elasticity

Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity relies upon the Continuum mechanics hypothesis and is applicable at macroscopic length scales....
. Good examples are a rubber band and a bouncing ball. This idea was first stated by Robert Hooke
Robert Hooke

Robert Hooke, Fellow of the Royal Society was an England natural philosopher and polymath who played an important role in the scientific revolution, through both experimental and theoretical work....
 in 1675 as a Latin anagram whose solution he published in 1678 as "Ut tensio, sic vis" which means "As the extension, so the force."

This linear relationship is called Hooke's law
Hooke's law

In mechanics, and physics, Hooke's law of theory of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit....
.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, elasticity is the physical property
Physical property

A physical property is any aspect of an object or substance that can be measurement or perception without changing its Identity . Physical properties can be Intensive and extensive properties....
 of a material when it deforms under stress
Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
 (e.g. external force
Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
s), but returns to its original shape when the stress is removed. The amount of deformation
Deformation

In materials science, deformation is a change in the shape or size of an object due to an applied force . This can be a result of tensile strength forces, compressive strength forces, Simple shear, bending or torsion ....
 is called the strain
Strain

Strain can refer to:* Strain , a variant of a plant, virus or bacterium; or an inbred animal used for experimental purposes* Strain , a chemical stress of a molecule...
.

Modeling elasticity


The elastic regime is characterized by a linear relationship between stress and strain, denoted linear elasticity
Linear elasticity

Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity relies upon the Continuum mechanics hypothesis and is applicable at macroscopic length scales....
. Good examples are a rubber band and a bouncing ball. This idea was first stated by Robert Hooke
Robert Hooke

Robert Hooke, Fellow of the Royal Society was an England natural philosopher and polymath who played an important role in the scientific revolution, through both experimental and theoretical work....
 in 1675 as a Latin anagram whose solution he published in 1678 as "Ut tensio, sic vis" which means "As the extension, so the force."

This linear relationship is called Hooke's law
Hooke's law

In mechanics, and physics, Hooke's law of theory of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit....
. The classic model of linear elasticity is the perfect spring
Spring (device)

A spring is an Elasticity object used to store mechanical energy. Springs are usually made out of hardened steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealing steel and hardened after fabrication....
. Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor
Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
, when considering simple situations of higher symmetry
Symmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance; such that it reflects beauty or perfection....
 such as a rod in one dimensional loading, the relationship may often be reduced to applications of Hooke's law.

Because most materials are elastic only under relatively small deformations, several assumptions are used to linearize the theory. Most importantly, higher order terms are generally discarded based on the small deformation assumption. In certain special cases, such as when considering a rubbery material, these assumptions may not be permissible. However, in general, elasticity refers to the linearized theory of the continuum stresses and strains.

Transitions to inelasticity


Above a certain stress known as the elastic limit or the yield strength
Yield (engineering)

The yield strength or yield point of a material is defined in engineering and materials science as the Stress at which a material begins to Plasticity ....
 of an elastic material, the relationship between stress and strain becomes nonlinear. Beyond this limit, the solid
Solid

A solid object is in the states of matter characterized by resistance to deformation and changes of volume. In other words, it has high values both of Young's modulus and of shear modulus; this contrasts e.g....
 may deform irreversibly, exhibiting plasticity
Plasticity (physics)

In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces....
. A stress-strain curve
Stress-strain curve

File:Metal yield.svgDuring testing of a material sample, the stress?strain curve is a graphical representation of the relationship between Stress , derived from measuring the load applied on the sample, and Strain , derived from measuring the deformation of the sample, i.e....
 is one tool for visualizing this transition.

Furthermore, not only solids exhibit elasticity. Some non-Newtonian fluid
Non-Newtonian fluid

A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo....
s, such as viscoelastic fluids
Viscoelasticity

Viscoelasticity is the property of materials that exhibit both Viscosity and Elasticity characteristics when undergoing Deformation. Viscous materials, like honey, resist shear flow and Strain linearly with time when a Stress is applied....
, 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
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
.

See also

  • Stiffness
    Stiffness

    Stiffness is the resistance of an Elasticity body to deformation by an applied force. It is an intensive and extensive properties....
  • Elastic modulus
    Elastic modulus

    An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it....
  • Linear elasticity
    Linear elasticity

    Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity relies upon the Continuum mechanics hypothesis and is applicable at macroscopic length scales....
  • Pseudoelasticity
    Pseudoelasticity

    Pseudoelasticity, or sometimes called superelasticity, is an Elasticity response to relatively high Stress caused by a phase transformation between the austenitic and martensitic phases of a crystal....
  • Viscoelasticity
    Viscoelasticity

    Viscoelasticity is the property of materials that exhibit both Viscosity and Elasticity characteristics when undergoing Deformation. Viscous materials, like honey, resist shear flow and Strain linearly with time when a Stress is applied....