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Pulp fibres are a part of the paper fibre network and contribute to its non‐linear rate‐dependent behaviour . An appropriate material model helps to quantify and understand these mechanisms, which are highly relevant to industry. The development of the constitutive equations is based on cyclic uniaxial tension tests . For that first a one dimensional viscoelastic, viscoplastic model was designed to fit experimental data. This one dimensional model is then ported to a three dimensional formulation with the logarithmic strain framework . The investigation shows that pulp fibres have a distinct plastic behaviour, which could be the cause of the non‐linear behaviour on the macroscopic level of the network.