We describe an efficient massively parallel implementation of our variant of the FETI type domain decomposition method called Total FETI with a lumped preconditioner. A special attention is paid to the discussion of several variants of parallelization of the action of the projections to the natural coarse grid and to the effective regularization of the stiffness matrices of the subdomains. Both numerical and parallel scalability of the proposed TFETI method are demonstrated on a 2D elastostatic benchmark up to 314,505,600 unknowns and 4800cores. The results are also important for implementation of scalable algorithms for the solution of nonlinear contact problems of elasticity by TFETI based domain decomposition method

The paper is devoted to 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 a closed form. This eliminates blind guesswork from the scheme and enables to analyze properties of the constitutive operator. It also simplifies the construction of the consistent tangent operator, which is important for the semismooth Newton method when applied to the incremental boundary‐value elastoplastic problem. The incremental problem in Mohr‐Coulomb plasticity is combined with limit load analysis. Beside a conventional direct method of 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.

The paper deals with numerical realization of discretized, frictionless static contact problems for elastic‐perfectly plastic materials and the computational limit analysis. Two numerical methods based on the variational formulation in terms of stresses are analyzed: the semi‐smooth Newton method with damping and the alternating direction method of multipliers. These methods are used for tracking the loadings path to determine the discretized limit loading parameter and for solving elastic‐perfectly plastic problems.