Mohr criterion

The Mohr failure criterion describing the conditions for which an isotropic material will fail, with any effect from the intermediate principal stress being neglected. Mohr can be written as a function of major and minor principal stresses, or normal stress and shear stress on the failure plane.

 

σ_e,t = σ₁ - X ⋅ σ₂

σ_e,c = 1/X ⋅ σ₁ - σ₂

 

or

 

σ_Mohr = τ_max

 

or

 

 

Where:

X = σ_u,t / σ_e,c

σ_e,t   – equivalent stress in tension;

σ_e,c  – equivalent stress in compression;

σ₁, σ₂  – principal stresses, σ₁ ≥ σ₂;

σ_e,c  – ultimate compression;

σ_u,t  – ultimate tension;

σ_Mohr  – radius of the Mohr's circle.