Editing Plasticity (physics) (section)

===Tresca criterion===
The Tresca criterion is based on the notion that when a material fails, it does so in shear, which is a relatively good assumption when considering metals. Given the principal stress state, we can use [[Mohr's circle]] to solve for the maximum shear stresses our material will experience and conclude that the material will fail if

: <math>\sigma_1 - \sigma_3 \ge \sigma_0</math>

where ''σ''<sub>1</sub> is the maximum normal stress, ''σ''<sub>3</sub> is the minimum normal stress, and ''σ''<sub>0</sub> is the stress under which the material fails in uniaxial loading. A [[yield surface]] may be constructed, which provides a visual representation of this concept. Inside of the yield surface, deformation is elastic. On the surface, deformation is plastic. It is impossible for a material to have stress states outside its yield surface.