Mixed stress-displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity

Abstract

We propose a mixed stress-displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von Mises plasticity. The discretization is based on isogeometric analysis (IGA) with non-uniform rational B-Splines (NURBS) as basis functions. As compared to conventional IGA Galerkin formulations, isogeometric collocation methods offer a high potential of computational cost reduction for higher-order discretizations as they eliminate the need for quadrature. In the proposed mixed formulation, both stress and displacement fields are approximated as primary variables with the aim of treating volumetric locking and instability issues, which occur in displacement-based isogeometric collocation for nearly incompressible elasticity and von Mises plasticity. The performance of the proposed approach is demonstrated by several numerical examples.