Remarks on a modified mixed least‐squares finite element formulation for small strain elasto‐plasticity

In this contribution a mixed least‐squares (LS) finite element formulation for rate‐independent elasto‐plasticity is presented within the framework of small deformations. Due to kink‐like points in the elasto‐plastic least‐squares functional, the variational approach yields to a discontinuous first variation and leads to problems by applying the standard Newton method. The proposed modification avoids this problem and guarantees the continuity of the modified weak form. We consider a least‐squares formulation, given through the balance of momentum, the constitutive equation and the consideration of an additional redundant stress symmetry condition, as a basis for the approach of a modification of the first variation. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)