An anisotropic in-plane and out-of-plane elasto-plastic continuum model for paperboard

A continuum model of paperboard material possessing a high degree of anisotropy is established. To handle the anisotropy, three vectors are introduced which phenomenologically represent the preferred directions of the material. The in-plane director vectors deform as line segments and the out-of-plane direction deforms as a normal vector. This allows for a decoupling of the in-plane and the out-of-plane responses in shearing. The model is developed for large plastic strains and consequently an expression for the plastic spin has been proposed. The choice of plastic spin allows for a control of the direction in which permanent deformations will occur. To show the predictive capabilities of the model, the important industrial process of creasing is simulated. Both the simplified line crease setup, as well as the actual rotation crease setup used in industrial applications are studied.