Geometry of principal stress trajectories for a Mohr-Coulomb material under plane strainстатья

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[1] Alexandrov S., Harris D. Geometry of principal stress trajectories for a mohr-coulomb material under plane strain // ZAMM Zeitschrift für Angewandte Mathematik und Mechanik. — 2017. — Vol. 97, no. 4. — P. 473–476. In the mechanics of granular and other materials the system of equations comprising the Mohr-Coulomb yield criterion together with the stress equilibrium equations under plane strain conditions forms a statically determinate system. The results presented here for this system are consequently independent of any flow rule that may be chosen to calculate the deformation and also independent of whether elastic strains are included. The stress equilibrium equations are written relative to a coordinate system in which the coordinate curves coincide with the trajectories of the principal stress directions. The general solution of the system is constructed relative to this coordinate system. A simple relation connecting the two scale factors for the coordinate curves is derived. In the special case that the angle of internal friction vanishes, this relation reduces to that already available for the Tresca yield criterion. A simple example is presented to illustrate the general solution. Finally, a boundary value problem for the region adjacent to an external boundary which coincides with a principal stress trajectory is formulated and its solution is outlined. [ DOI ]

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