Finite Elements in Analysis and Design, Volume 47, Issue 7, July 2011
New finite elements comprising parts (rods and spiral springs) with independent behaviors, which can be determined from the corresponding independent experiments – shear, deviatoric loading, hydrostatic loading – are suggested for isotropic material in 2D and 3D cases and applied for solving some problems for cohesive-frictional material. The material is assumed to be non-linear with the stress–strain relationship of hyperbolic type and failure conditions determined by Mohr–Coulomb law. The difficulty of the problems consists in the fact that the limit stresses themselves depend on unknown stress distribution, so a stress–strain equation cannot be written in the explicit form before solving the problem. This difficulty is avoided by iterations: a suitable initial stress distribution (e. g. from the corresponding elastic problem) is supposed and, knowing the material properties, the new stress distribution (appearing as a result of slow gradual load application) can be found which is taken as the initial for the next iteration, and so on. The following two problems are considered: failure of a horizontal layer under action of a uniform pressure applied to a rectangular area on the layer surface and the problem of slope stability.
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