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φ' = the effective stress friction angle, or the 'angle of internal friction' after Coulomb friction. The coefficient of friction is equal to tan(φ'). Different values of friction angle can be defined, including the peak friction angle, φ' p, the critical state friction angle, φ' cv, or residual friction angle, φ' r.
The Mohr–Coulomb theory is named in honour of Charles-Augustin de Coulomb and Christian Otto Mohr.Coulomb's contribution was a 1776 essay entitled "Essai sur une application des règles des maximis et minimis à quelques problèmes de statique relatifs à l'architecture" .
The two regimes of dry friction are 'static friction' ("stiction") between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces. Coulomb friction, named after Charles-Augustin de Coulomb , is an approximate model used to calculate the force of dry friction.
This theory is exact for the situation of an infinite friction coefficient in which case the slip area vanishes, and is approximative for non-vanishing creepages. It does assume Coulomb's friction law, which more or less requires (scrupulously) clean surfaces. This theory is for massive bodies such as the railway wheel-rail contact.
Mayniel (1808) [18] later extended Coulomb's equations to account for wall friction, denoted by . Müller-Breslau (1906) [19] further generalized Mayniel's equations for a non-horizontal backfill and a non-vertical soil-wall interface (represented by an angle from the vertical).
Expressions in terms of cohesion and friction angle [ edit ] Since the Drucker–Prager yield surface is a smooth version of the Mohr–Coulomb yield surface , it is often expressed in terms of the cohesion ( c {\displaystyle c} ) and the angle of internal friction ( ϕ {\displaystyle \phi } ) that are used to describe the Mohr–Coulomb yield ...
Another choice is to intersect the Mohr–Coulomb yield surface at four vertices on both axes (uniaxial fit) or at two vertices on the diagonal = (biaxial fit). [28] The Drucker-Prager yield criterion is also commonly expressed in terms of the material cohesion and friction angle.
As shown in Figure 6, to determine the stress components (,) acting on a plane at an angle counterclockwise to the plane on which acts, we travel an angle in the same counterclockwise direction around the circle from the known stress point (,) to point (,), i.e., an angle between lines ¯ and ¯ in the Mohr circle.