Continuum modeling of paperboard for the mechanical response of converting processes

Sammanfattning: Paperboard is a thin and lightweight material made of cellulose fibers and it is an important component in packaging material where it provides stiffness and rigidity. The scope of this work is the development of continuum models, and its numerical treatments, for simulating the processes of converting paperboard into packages. The thesis begins with a general introduction to paperboard and a review of modeling approaches are presented. Important continuum modeling concepts used in the papers are presented and key paperboard converting processes are discussed. The main part of the thesis consists of four papers denoted A, B, C and D and they are briefly outlined below.To reduce the computational effort during large scale paperboard forming simulations, a numerical technique which combines a state-of-the-art continuum model for paperboard with state-of-the-art finite element modeling is investigated in Paper A. The model is built up by solid-shell elements where the thickness direction is naturally included in the framework such that the out-of-plane response can be modeled. The approach is validated by numerical studies where the results are compared against fully integrated brick elements. Furthermore, a large-scale forming example for paperboard is explored. Since the loading rate varies during industrial processes and the aim is to maximize the operational velocity, a rate-dependent continuum model for paperboard is developed in Paper B. The new rate-dependent model is based on the static material model in Paper A which is enhanced with a viscoelastic and viscoplastic framework. The developed model is calibrated using uniaxial experiments and evaluated against line-creasing and line-folding measurements. In Paper C, the continuum model in Paper A is enhanced to include continuum damage. Damage is needed to adequately capture the mechanical response during sequential loading of creasing and folding. A scalar isotropic damage variable is introduced and the damage evolution is calibrated for a reference mesh during folding. A simple scaling strategy is introduced to reduce the mesh dependence due to damage evolution. To showcase the proposed model, an illustrative $3$D example is presented where a paperboard sheet is creased and folded to mimic the corner folding process. In Paper D, an experimental device and a protocol is developed for cyclic uniaxial out-of-plane compression and tension measurements. This load case is important since it is present during creasing and subsequent folding where the material is subject to large out-of-plane compressive stresses followed by out-of-plane tension and delamination. The soft initial load-displacement response during compression is shown to stem from the surface roughness and not a material property. In addition, the experiments show that the transition from compression to tension is smooth. Consequently, a switch function, previously introduced in literature that separates the elastic behavior between compression and tension, is deemed as questionable for continuum modeling.