| 373 |
elastic modulus.
there are three main elastic moduli: Young's, Shear,
which measures the resistance to motion of the planes
of a solid sliding past each other, bulk.
|
\[
\mathrm{elastic\ modulus}\equiv\frac{\mathrm{stress}}{\mathrm{strain}}
\]
|
| 373 |
elastic limit
|
|
| 373 |
tensile stress
|
\[
\mathrm{tensile\ stress}=\frac{F}{A}
\]
|
| 373 |
tensile strain
|
\[
\mathrm{tensile\ strain}=\frac{\Delta L}{L_i}
\]
|
| 374 |
shear stress,
where $F=$ tangential force
|
\[
\mathrm{shear\ stress}=\frac{\Delta x}{h}
\]
|
| 374 |
shear strain
|
\[
\mathrm{shear\ strain}=\frac{\Delta x}{h}
\]
|
| 374 |
volume stress,
$F=$ normal force
|
\[
\mathrm{volume\ stress}=\frac{F}{A}=P
\]
|
| 374 |
volume strain
|
\[
\mathrm{volume\ strain}=\frac{\Delta V}{V_i}
\]
|
| 373 |
Young's (tensile) modulus.
elastic modulus that measures resistance of a solid to a change in its length
|
\[
Y=\frac{\mathrm{tensile\ stress}}{\mathrm{tensile\ strain}}=\frac{F/A}{\Delta L/L_i}
\]
|
| 374 |
shear modulus.
elastic modulus that measures resistance to motion of the planes of a solid sliding past each other.
|
\[
S=\frac{\mathrm{shear\ stress}}{\mathrm{shear\ strain}}=\frac{F/A}{\Delta x /h}
\]
|
| 374 |
bulk modulus.
elastic modulus which measures the resistance of solids or liquids to changes in their volume.
|
\[
\begin{align*}
B &\equiv\frac{\mathrm{volume\ stress}}{\mathrm{volume\ strain}}\\
&=-\frac{\Delta F / A}{\Delta V / V_i}
=-\frac{\Delta P}{\Delta V / V_i}
\end{align*}
\]
|
Alex Notes