The mixed complementarity problem arising from non-associative plasticity with non-smooth yield surfaces

An elastic domain with multiple yield surfaces brings about huge troubles to numerical computations due to singularities, while non-associative plasticity leads further to the open issue of whether constitutive integration is well posed. This study reduces the constitutive integration of non-associative plasticity with multiple yield surfaces to a mixed complementarity problem, represented by MiCP, a special case of finite-dimensional variational inequalities. By means of the projection- contraction algorithm for finite-dimensional variational inequalities and the idea of the Gauss-Seidel method, a new projection-contraction algorithm for MiCP is designed and denoted by GSPC. Applying the monotonicity of the mapping of the MiCP, GSPC is proved convergent theoretically for associative plasticity. For non-associative plasticity, the sufficient condition for GSPC to be convergent is also established if the tension part of the Mohr-Coulomb elastic domain is cut off. Typical examples are designed to illustrate GSPC is highly efficient, accurate and stable, some of which cannot be solved by the conventional return-mapping method. In all the cases, the computational efficiency of GSPC is apparently above the mapping return method. (C) 2019 Elsevier B.Y. All rights reserved.