# Difference between revisions of "Viscoelastic"

## 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 ($\sigma$) is given by the applied force over the area, namely $\sigma = F/A$, and the shear strain ($e$) is given by $e = \Delta x/y$. 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 ($G$), $\sigma = Ge$.

## 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 ($\eta$), $\sigma = \eta \dot{e}$.

## Example

Since viscoelastic behavior comes in various forms,