Stress (Mechanics)
#Physics
Topics
$\displaystyle \sigma=\frac{F}{A}=E\varepsilon$
- Different from pressure in that the forces are internal to the object
- $\displaystyle F$ is the axial forcex
- $\displaystyle E$ is Young's Modulus
- $\displaystyle \varepsilon$ is strain
$$
\sigma=\begin{bmatrix}
{\sigma}{11} & \sigma{12} & \sigma_{13} \\\sigma_{21} & \sigma_{22} & \sigma_{23} \\\sigma_{31} & \sigma_{32} & \sigma_{33}
\end{bmatrix}
$$
- From this video
- A rank 2 tensor in 3D
- Each column represents the traction experienced by face $\displaystyle j$ in direction $\displaystyle i$ for a given $\displaystyle \sigma_{ij}$
- The matrix must be symmetric for rotational equilibrium to be preserved (i.e. no rotational acceleration)