surface in Haigh–Westergaard space The Mohr–Coulomb failure (yield) surface is often expressed in Haigh–Westergaad coordinates. For example, the function can be expressed as Alternatively, in terms of the invariants we can write where {| class="toccolours collapsible collapsed" width="80%" style="text-align:left" !Derivation of alternative forms of Mohr–Coulomb yield function |- |We can express the yield function as The Haigh–Westergaard invariants are related to the principal stresses by Plugging into the expression for the Mohr–Coulomb yield function gives us Using trigonometric identities for the sum and difference of cosines and rearrangement gives us the expression of the Mohr–Coulomb yield function in terms of . We can express the yield function in terms of by using the relations and straightforward substitution. |} Mohr–Coulomb yield and plasticity The Mohr–Coulomb yield surface is often used to model the plastic flow of geomaterials (and other cohesive-frictional materials). Many such materials show dilatational behavior under triaxial states of stress which the Mohr–Coulomb model does not include. Also, since the yield surface has corners, it may be inconvenient to use the original Mohr–Coulomb model to determine the direction of plastic flow (in the flow theory of plasticity). A common approach is to use a non-associated plastic flow potential that is smooth. An example of such a potential is the function where is a parameter, is the value of when the plastic strain is zero (also called the initial cohesion yield stress), is the angle made by the yield surface in the Rendulic plane at high values of (this angle is also called the dilation angle), and is an appropriate function that is also smooth in the deviatoric stress plane. Typical values of cohesion and angle of internal friction Cohesion (alternatively called the cohesive strength) and friction angle values for rocks and some common soils are listed in the tables below. See also 3-D elasticity Hoek–Brown failure criterion Byerlee's law Lateral earth pressure von Mises stress Yield (engineering) Drucker Prager yield criterion — a smooth version of the M–C yield criterion Lode coordinates References https://web.archive.org/web/20061008230404/http://fbe.uwe.ac.uk/public/geocal/SoilMech/basic/soilbasi.htm http://www.civil.usyd.edu.au/courses/civl2410/earth_pressures_rankine.doc Solid mechanics Soil mechanics Plasticity (physics) Materials science Applied mathematics Yield criteria