Difference between revisions of "Viscoelastic"
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==Definition== | ==Definition== | ||
| − | A substance that displays behavior that is both viscous and elastic is said to be '''viscoelastic'''. In this sense, viscoelastic materials are said to be a combination of the | + | A substance that displays behavior that is both viscous and elastic is said to be '''viscoelastic'''. In this sense, viscoelastic materials are said to be a combination of the (elastic) Hookean solid and the (viscous) Newtonian liquid, with a response to shear stress dependent on time (i.e. viscoelastic substances react in a time-dependent manner to a constant applied shear stress). |
==Hookean Solid== | ==Hookean Solid== | ||
| − | A Hookean solid is | + | A Hookean solid is a solid that displays perfectly elastic behavior. This corresponds to the fact that an applied shear stress produces a constant shear strain in response. Recall that the shear stress (<math>\sigma</math>) is given by the applied force over the area, namely <math>\sigma = F/A</math>, and the shear strain (<math>e</math>) is given by <math>e = \Delta x/y</math>. See Figure 1 for clarification. |
| − | [[Image:Cube. | + | [[Image:Cube.png|thumb|Figure 1, taken from reference [1]]] |
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| + | For a Hookean solid, we simply have the shear stress proportional to the applied stress by a proportionality constant called the shear modulus (<math>G</math>), <math>\sigma = Ge</math>. This type of solid obeys Hooke's law for any magnitude of applied stress. | ||
==Newtonian Liquid== | ==Newtonian Liquid== | ||
| + | In the case of a Newtonian liquid, the shear stress is proportional to the first time derivative of the shear strain by a constant called the viscosity (<math>\eta</math>), <math>\sigma = \eta \dot{e}</math>. | ||
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| + | One deviation from a Newtonian liquid is a liquid that has a viscosity that is dependent on shear rate, such that <math>\sigma = \eta (\dot{e}) \dot{e}</math>. | ||
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| + | ==Examples== | ||
| + | Since viscoelastic behavior comes in various forms that (in general) need to be treated individually, it is instructive to look at a simple example. | ||
| + | |||
| + | In Figure 2, a shear stress is initially applied at time <math>t = 0</math> and is held constant. The material initially acts in an elastic (Hookean solid) manner (i.e. there is a constant strain response to a constant shear stress) until the relaxation time <math>\tau</math>, after which it reacts to the applied stress in the same way a Newtonian liquid would (i.e. there is a linearly increasing shear strain response to a constant shear stress). In this sense, the relaxation time for a viscoelastic material under a particular applied stress separates when the material acts like a solid, and when it acts like a liquid. | ||
| + | |||
| + | [[Image:Example.png|thumb|Figure 2, taken from reference [1]]] | ||
| + | Another (more fun) example can be found here: [http://www.youtube.com/watch?v=f2XQ97XHjVw Viscoelastic Example]. In this video, a large amount of cornstarch and water have been mixed together to form a non-Newtonian liquid. As demonstrated, a short applied stress (quickly running across the material) results in an elastic response, whereas a long applied stress (standing on the material) results in a viscous response. | ||
==References== | ==References== | ||
| + | [1] R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002). | ||
Latest revision as of 06:13, 14 September 2009
Definition
A substance that displays behavior that is both viscous and elastic is said to be viscoelastic. In this sense, viscoelastic materials are said to be a combination of the (elastic) Hookean solid and the (viscous) Newtonian liquid, with a response to shear stress dependent on time (i.e. viscoelastic substances react in a time-dependent manner to a constant applied shear stress).
Hookean Solid
A Hookean solid is a solid that displays perfectly elastic behavior. This corresponds to the fact that an applied shear stress produces a constant shear strain in response. Recall that the shear stress (<math>\sigma</math>) is given by the applied force over the area, namely <math>\sigma = F/A</math>, and the shear strain (<math>e</math>) is given by <math>e = \Delta x/y</math>. See Figure 1 for clarification.
For a Hookean solid, we simply have the shear stress proportional to the applied stress by a proportionality constant called the shear modulus (<math>G</math>), <math>\sigma = Ge</math>. This type of solid obeys Hooke's law for any magnitude of applied stress.
Newtonian Liquid
In the case of a Newtonian liquid, the shear stress is proportional to the first time derivative of the shear strain by a constant called the viscosity (<math>\eta</math>), <math>\sigma = \eta \dot{e}</math>.
One deviation from a Newtonian liquid is a liquid that has a viscosity that is dependent on shear rate, such that <math>\sigma = \eta (\dot{e}) \dot{e}</math>.
Examples
Since viscoelastic behavior comes in various forms that (in general) need to be treated individually, it is instructive to look at a simple example.
In Figure 2, a shear stress is initially applied at time <math>t = 0</math> and is held constant. The material initially acts in an elastic (Hookean solid) manner (i.e. there is a constant strain response to a constant shear stress) until the relaxation time <math>\tau</math>, after which it reacts to the applied stress in the same way a Newtonian liquid would (i.e. there is a linearly increasing shear strain response to a constant shear stress). In this sense, the relaxation time for a viscoelastic material under a particular applied stress separates when the material acts like a solid, and when it acts like a liquid.
Another (more fun) example can be found here: Viscoelastic Example. In this video, a large amount of cornstarch and water have been mixed together to form a non-Newtonian liquid. As demonstrated, a short applied stress (quickly running across the material) results in an elastic response, whereas a long applied stress (standing on the material) results in a viscous response.
References
[1] R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).
