Modified Mohr Theory

Modified Mohr theory is a modicfication of Coulomb-Mohr Theory for brittle materials. We will only consider plane stress and not the general 3D case.

Plane Stress

For plane stress, we have two principal stresses in the plane of analysis, such that ${\sigma }_A\ge {\sigma }_B$. The third principal stress is zero. We have 4 cases:

Case 1 & 2: $[{\sigma }_A\ge {\sigma }_B\ge 0]$ and $[{\sigma }_B/{\sigma }_A]>1$:

Case 3: ${\sigma }_A\ge 0\ge {\sigma }_B$ and $|{\sigma }_B/{\sigma }_A|>1$

$$\frac{(S_{uc}-S_{ut}){\sigma }_A}{S_{uc}{S}_{ut}}-\frac{{\sigma }_B}{S_{uc}}\ge 1$$

and

$$\frac{(S_{uc}-S_{ut}){\sigma }_A}{S_{uc}{S}_{ut}}-\frac{{\sigma }_B}{S_{uc}}=\frac{1}{n}$$

Case 4: $0\ge {\sigma }_A\ge {\sigma }_B$:

$$\begin{array}{r}{\sigma }_B\le -S_{uc}\\ {\sigma }_B=-\frac{S_{uc}}{n}\end{array}$$