Modeling the effect of creep in paper fibres under the influence of external loading and changes in moisture

Paper is a material exhibiting a complex microstructure that is composed of a network of fibres at the micro-level. When subjected to external loading or variations in moisture conditions over different time scales, changes in strain that are non-linear with respect to time are observed at the sheet level (macro-scale). In order to investigate this time-dependent behaviour of paper, a creep power law model is implemented within a finite element approach at the level of single fibres. This rate-dependent model is found to capture experimental results available in literature for single fibres with a good agreement (both quantitatively and qualitatively). Based on the identified model at the level of single fibres, the time-dependent hygro-mechanical response is upscaled towards the network scale. To this end, random model networks of ribbon shaped fibres are generated and their response is simulated. The network-scale response, emerging from the rate-dependent fibre model, demonstrates the ability to predict the response of networks subjected to relaxation at a constant moisture level. The developed numerical model predicts lower values of overall stress response in single fibres as compared to networks. Also, stress relaxation predicted by the rate-dependent model in the cross-direction of the networks is in agreement with the experimental observations by Johanson and Kubát (1967). Therefore, one of the remarkable findings of the present work is that the developed rate-dependent model is robust enough to capture the sheet scale response also qualitatively. Based on the study of these computational results, a better understanding is achieved regarding the influence of mechanical and rate-dependent properties of single fibres on the hygro-expansion of complete fibre networks, and in particular of paper sheets.