# Difference between revisions of "Viscoelastic"

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A Hookean solid is one that displays perfectly elastic behavior. This corresponds to the fact that an applied shear stress produces a 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. | A Hookean solid is one that displays perfectly elastic behavior. This corresponds to the fact that an applied shear stress produces a 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.png|thumb|Figure 1]] | + | [[Image:Cube.png|thumb|Figure 1, taken from reference [1]]] |

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>. | 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>. | ||

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==Example== | ==Example== | ||

− | Since viscoelastic behavior comes in various forms, | + | Since viscoelastic behavior comes in various forms, it is instructive to look at a simple example. |

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+ | In Figure 2, | ||

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+ | [[Image:Example.png|thumb|Figure 2, taken from reference [1]]] | ||

==References== | ==References== |

## Revision as of 17:26, 12 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 ideal (elastic) Hookean solid and the (viscous) Newtonian liquid, along with a time a dependence.

## Hookean Solid

A Hookean solid is one that displays perfectly elastic behavior. This corresponds to the fact that an applied shear stress produces a 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>.

## 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>.

## Example

Since viscoelastic behavior comes in various forms, it is instructive to look at a simple example.

In Figure 2,