Stress and Strain

Stress = Force per unit area
Strain = fractional change in the solid

  • $$\frac{\Delta L}{L_0}$$ = linear (stretch/compress) strain
  • $$\frac{\Delta X}{L_0}$$ = shear (sideways) strain

  • $$\frac{\Delta V}{V_0}$$ = bulk (volume) strain

Stress $$\propto$$ Strain:

$$ \begin{eqnarray*} F & = & {\cal Y} \quad {{\Delta L}\over L_0} \quad A, \qquad {\cal Y} = \mbox{Young's modulus} \\ F & = & {\cal S} \quad {{\Delta X}\over L_0} \quad A, \qquad {\cal S} = \mbox{shear modulus} \\ P = {F}/{A} & = & - {\cal B} \quad \frac{\Delta V}{V_0} , \qquad {\cal B} = \mbox{bulk modulus} \end{eqnarray*} $$