  The paper is devoted to a constitutive solution, limit load analysis and
Newton-like methods in elastoplastic problems containing the Mohr-Coulomb yield
criterion. Within the constitutive problem, we introduce a self-contained
derivation of the implicit return-mapping solution scheme using a recent
subdifferential-based treatment. Unlike conventional techniques based on
Koiter's rules, the presented scheme a priori detects a position of the unknown
stress tensor on the yield surface even if the constitutive solution cannot be
found in closed form. This fact eliminates blind guesswork from the scheme,
enables to analyze properties of the constitutive operator, and simplifies
construction of the consistent tangent operator which is important for the
semismooth Newton method applied on the incremental boundary value
elastoplastic problem. The incremental problem in Mohr-Coulomb plasticity is
combined with the limit load analysis. Beside a conventional direct method of
the incremental limit analysis, a recent indirect one is introduced and its
advantages are described. The paper contains 2D and 3D numerical experiments on
slope stability with publicly available Matlab implementations.
