A non-associative orthotropic plasticity model for paperboard under in-plane loading

In this paper, we present an in-plane yield criterion using sub-surfaces that are related to the orthotropic material axes of paperboard. A non-associative flow rule is proposed to decouple the plastic volumetric strain response from the yield surface’s shape. This offers adaptability of both, the yielding under biaxial tension and the plastic Poisson’s ratios under tension and compression. Anisotropic hardening is introduced by making use of the sub-surface structure of the yield surface formulation. In addition, a scaling function for shear hardening is introduced in order to describe the material behaviour under compressive loading with superimposed shear. Off-axis tensile and compression tests were performed to determine the necessary material parameters. Hereby, significant differences were found between the plastic Poisson’s ratios under tension and compression. To account for local variations in paperboard density, a homogenization on basis of transmitted light images is suggested and applied to strain measurements by digital image correlation.