Difference between revisions of "Elasticity and molecular properties"
(→Elasticity) |
(→Elasticity) |
||
Line 3: | Line 3: | ||
== Elasticity == | == Elasticity == | ||
− | A material becomes deformed when a stress is applied to it. Its elasticity is the material's ability to return to its original form once the stress is removed. This way the deformation of the material occurs follows Hooke's law: it is proportional to the stress up until a certain point, which is called the elastic limit. Any additional stress applied after the elastic limit has been reached, the material becomes permanently deformed -- it cannot return to its original shape. When stresses are so large that Hooke's law is no longer satisfied, we are talking about the nonlinear region. | + | A material becomes deformed when a stress is applied to it. Its elasticity is the material's ability to return to its original form once the stress is removed. This way the deformation of the material occurs follows Hooke's law: it is proportional to the stress up until a certain point, which is called the elastic limit. Any additional stress applied after the elastic limit has been reached, the material becomes permanently deformed -- it cannot return to its original shape. When stresses are so large that Hooke's law is no longer satisfied, we are talking about the nonlinear region. In the linear region, where Hooke's law does apply, we see that the graph of elasticity versus stress is linear. After the elastic limit it becomes curved and decisively non-linear. |
{| class="wikitable" border="1" | {| class="wikitable" border="1" |
Revision as of 19:49, 21 September 2008
Elasticity
A material becomes deformed when a stress is applied to it. Its elasticity is the material's ability to return to its original form once the stress is removed. This way the deformation of the material occurs follows Hooke's law: it is proportional to the stress up until a certain point, which is called the elastic limit. Any additional stress applied after the elastic limit has been reached, the material becomes permanently deformed -- it cannot return to its original shape. When stresses are so large that Hooke's law is no longer satisfied, we are talking about the nonlinear region. In the linear region, where Hooke's law does apply, we see that the graph of elasticity versus stress is linear. After the elastic limit it becomes curved and decisively non-linear.
,, | |
Since work is required to stretch a solid and the modulus is an energy per unit volume; or the modulus must be related to molecular interactions.
"Meaning" of elasticity
For small stresses on solids or for short times on liquid: | |
Energy stored per unit volume: | |
G has units of energy/volume. For "soft" matter: |
Spring model of intemolecular interaction
The multiple-spring model is combined with the potential energy model to calculate a molecular model of elasticity:
Material | Bond enery | Distance | Modulus |
---|---|---|---|
Metals | 100kT | About 1 Ang | 10^12 Pa |
Soft materials | 1kT | About 10 nm | 10^3 Pa |