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In [[materials science]] and [[continuum mechanics]], '''viscoelasticity''' is the property of [[materials]] that exhibit both [[Viscosity|viscous]] and [[Elasticity (physics)|elastic]] characteristics when undergoing [[deformation (engineering)|deformation]]. Viscous materials, like water, resist both [[shear flow]] and [[Strain (materials science)|strain]] linearly with time when a [[Stress (physics)|stress]] is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.
Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent stress and strain. Whereas elasticity is usually the result of [[chemical bond|bond]] stretching along [[crystallographic plane]]s in an ordered solid, viscosity is the result of the diffusion of atoms or molecules inside an [[amorphous]] material.<ref name=Meyers>Meyers and Chawla (1999): "Mechanical Behavior of Materials", 98-103.</ref>
==Background==
In the nineteenth century, physicists such as [[James Clerk Maxwell]], [[Ludwig Boltzmann]], and [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] researched and experimented with [[Creep (deformation)|creep]] and recovery of [[glass]]es, [[metal]]s, and [[rubber]]s. Viscoelasticity was further examined in the late twentieth century when [[synthetic polymer]]s were engineered and used in a variety of applications.<ref name=McCrum>McCrum, Buckley, and Bucknell (2003): "Principles of Polymer Engineering," 117-176.</ref>
Viscoelasticity calculations depend heavily on the [[viscosity]] variable, ''η''. The inverse of ''η'' is also known as [[Viscosity#Fluidity|fluidity]], ''φ''. The value of either can be derived as a [[Temperature dependence of liquid viscosity|function of temperature]] or as a given value (i.e. for a [[dashpot]]).<ref name="Meyers" /> [[Image:Non-Newtonian fluid.svg|thumb|350px| Different types of responses {{nowrap|(<math>\sigma</math>)}} to a change in strain rate {{nowrap|(<math>d\varepsilon/dt</math>)}}]]
Depending on the change of strain rate versus stress inside a material, the viscosity can be categorized as having a linear, non-linear, or plastic response
* When a material exhibits a linear response it is categorized as a Newtonian material. In this case the stress is linearly proportional to the strain rate. * If the material exhibits a non-linear response to the strain rate, it is categorized as [[non-Newtonian fluid]]. * There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. A material which exhibits this type of behavior is known as [[thixotropy|thixotropic]]. * In addition, when the stress is independent of this strain rate, the material exhibits plastic deformation.<ref name="Meyers" /> Many viscoelastic materials exhibit [[rubber]] like behavior explained by the thermodynamic theory of polymer elasticity. Some examples of viscoelastic materials are amorphous polymers, semicrystalline polymers, biopolymers, metals at very high temperatures, and bitumen materials. Cracking occurs when the strain is applied quickly and outside of the elastic limit. [[Ligament]]s and [[tendon]]s are viscoelastic, so the extent of the potential damage to them depends on both the rate of the change of their length and the force applied.{{Citation needed|reason=maybe https://doi.org/10.1114/1.1408926| date=February 2017}}
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