Explaining irreversible hygroscopic strains in paper: a multi-scale modelling study on the role of fibre activation and micro-compressions

This paper proposes a meso-structural model for the discrete fibrous network of paper, which is able to upscale the irreversible phenomena from the underlying hygro-mechanics towards the effective behaviour at the macro-scale. The swelling of individual fibres, induced by moisture content variations, is transmitted to the network through inter-fibre bonds and governs the resulting effective material response. The present approach is based on a recently developed discrete meso-structural model for the reversible part of the response, which distinguishes between the influence on the hygroscopic behaviour of free-standing fibre segments and inter-fibre bonds. The network structure, fibre and bond geometries and hygro-elastic properties are explicitly incorporated. The major novelty of this contribution is the extended fibre constitutive model, enabling to describe some typical irreversible mechanisms and instability effects related to the history of the manufacturing. This extension strongly affects the effective material behaviour beyond the elastic range. Despite the valuable work in the literature, no papers can be found dedicated to meso-structural models including these phenomena. Using an appropriate homogenization strategy, the unit-cell is solved analytically, capturing irreversible shrinkage in restrained dried paper and the occurrence of local buckling within the bond for freely dried material. The proposed scale transition offers a deeper insight into the complex relation between the events occurring at the different length scales. The potential of the proposed methodology is demonstrated through the convincing agreement with experimental data obtained from the literature.