Finite elements for cohesive-frictional material

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. (C) 2011 Elsevier B.V. All rights reserved.