[[Poisson's Ratio|Poisson’s ratio]], [[Hooke's Law|Young’s modulus]], and the [[Engineering Shear Strain|modulus of rigidity]] are all related to each other. As such, knowing only two of the material properties allows the third to be derived. $G=\dfrac{E}{2(1+\nu)}$ To summarize, the following equations fully describe the relationship between [[Stress|stress]] and [[Strain|strain]] for small deformations: $\varepsilon_x=\dfrac{\sigma_x}{E}−\nu\dfrac{\sigma_y}{E}−\nu\dfrac{\sigma_z}{E}$ $\varepsilon_y=\dfrac{\sigma_y}{E}−\nu\dfrac{\sigma_x}{E}−\nu\dfrac{\sigma_z}{E}$ $\varepsilon_z=\dfrac{\sigma_z}{E}−\nu\dfrac{\sigma_x}{E}−\nu\dfrac{\sigma_y}{E}$ $\gamma_{xy}=\dfrac{2(1+\nu)}{E}\tau_{xy}$ $\gamma_{xz}=\dfrac{2(1+\nu)}{E}\tau_{xz}$ $\gamma_{yz}=\dfrac{2(1+\nu)}{E}\tau_{yz}$ Understand that: $\gamma_{ij}=2\varepsilon_{ij}$ The above relationships can be derived directly from [[Hooke's Law]].