Limit State Analysis of Paper and Paperboard

• Applicant: Professor Dr.-Ing. Jaan-Willem Simon
• Subject Area: Applied Mechanics, Statics and Dynamics ; Mechanics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545144829

Paper and paperboard are gaining importance in numerous technically relevant applications, in particular in the packaging industry, because they are extremely versatile, renewable materials and easily recyclable. It is expected that the relevance of these materials will soar over the coming years, since paper and paperboard are increasingly used as substitutes for single-use plastic products. Even though paper has been in use for approximately 2000 years, its material behaviour is still not sufficiently understood, and its modelling is underdeveloped. The challenge in the material modelling of paper is its multiscale nature. On the macroscale, paper shows a distinct elasto-plastic behaviour. While this behaviour is well-understood for engineering materials such as metals, where mechanisms like plastic slip on the microstructure are known to result in plasticity on the macroscale, such effects are drastically different in paper. The reason that paper is so fundamentally different is the intrinsic microstructure, which consists of an unstructured fibre network. This fibre network structure dictates the macroscale material response. The elasto-plastic behaviour of single fibres, the breaking of individual fibres and fibre bonds, and friction between fibres result in what appears to be a combination of elasto-plasticity and damage on the macroscale, where the elasto-plasticity is the by far dominating driver for most practical applications. Moreover, for metals and several other materials, limit states of the material and their structures are well-known and understood, even for loading scenarios that vary over time – e.g. cyclically. Such limit states are defined as the maximum loading state at which the system can still be considered ‘safe’ and will not fail due to alternating plasticity (plastic deformations with changing signs and low overall plastic strains leading to low cycle fatigue); nor will the system fail due to incremental plastic collapse (continuously growing plastic deformations leading to failure even after low numbers of cycles). These safe states are referred to as ‘shakedown’. Computing those limit states in terms of the structural load bearing capacity is an important and challenging task for construction engineers in structural design. Until now, the limit state analysis of paper and paperboard structures has not been addressed at all, although the existence of shakedown phenomena similar to the ones in e.g. metals is to be expected. Thus, the aim of this project is to scrutinise the limit states of paper and paperboard structures. The findings will be built into a computational tool with a view to analysing the limit states of paper and paperboard. The final outcome of this project will be a numerical toolbox for limit and shakedown analysis, so that paper-made structures can be designed and optimised for safe structural performance.

• DFG Programme: Research Grants