Stress (mechanics)

Topics

• Shear Stress
• Mohr’s Circle
• Principal Stress
• Stress on Mesh

$\sigma =\frac{F}{A}=E\epsilon$

• Different from pressure in that the forces are internal to the object
• $F$ is the axial forcex
• $E$ is Young’s Modulus
• $\epsilon$ is strain

$$\sigma =\left[\begin{array}{ccc}{\sigma }_{11}& {\sigma }_{12}& {\sigma }_{13}\\ {\sigma }_{21}& {\sigma }_{22}& {\sigma }_{23}\\ {\sigma }_{31}& {\sigma }_{32}& {\sigma }_{33}\end{array}\right]$$

• From this video
• A rank 2 tensor in 3D
• Each column represents the traction experienced by face $j$ in direction $i$ for a given ${\sigma }_{ij}$
  
• The matrix must be symmetric for rotational equilibrium to be preserved (i.e. no rotational acceleration)