# Mohr-Coulomb theory

1. Nov 5, 2005

### Mk

What is the Mohr-Coulomb theory? Can you tell me a bit about it?

2. Nov 20, 2005

### PerennialII

Are you referring to the frictional plasticity theory ?

3. Nov 20, 2005

### Mk

I think so, yes.

4. Nov 21, 2005

### PerennialII

About the model in general ...... if you've some specifics in mind "shoot"....

For materials like soil, rock etc. frictional and dilatational effects need to be incorporated in the constitutive modeling (think about deformation of concrete intuitively as an example, the role of friction in the plasticity response is somewhat easy to "visualize"). Standard J2 - von Mises type of yield criterion & flow rule & evolution equation don't generally produce decent results when applied to such materials, when they neglect both frictional and pressure sensitive (dilatational) effects to plastic deformation.

So, in order to get rid of this handicap pressure dependent material models for plasticity have been developed. The yielding conditions for example have frictional resistance term(s), in the Mohr-Coulomb case the yield condition states that yielding occurs when a critical combination of shear stress and mean normal stress are reached on any plane, the criterion written as - for the magnitude of the shear stress for yield
$$\tau=c-\mu\sigma$$
$\sigma$ is the normal stress on a plane, c is the cohesion shear stress, and the "coefficient of internal friction" is defined via an angle of internal friction (-> next sentence). Essentially you can understand the yield criterion being wedge shaped (its cross-section) with an angle identified with the friction coefficient (when viewed in a plane) as a function of mean normal stress (a dependency standard von Mises for example doesn't have). A related, and a "better behaving" model is the Drucker-Prager model (similar analogy in the shape of the yield surface as between Tresca and von Mises models) - which for this reason have usually used in numerical work.

A pretty 'solid' presentation:
http://www.granular-volcano-group.org/frictional_theory.html#II.