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

Abstract

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.