The compressive response of a stratified fibrous structure

A model for the compressive response of an oriented fiber structure such as paper is derived in this work. The model provides a semi-quantitative description of the stress/strain behavior of a fiber structure. The model accounts for the deformation of fibers during compression, their finite fiber length, their elastic modulus, and their moment of inertia. Using a previously describe micro-indentation technique, the predicted impact of variables used in the model on the compressive response of paper is verified. Results consistent with the model are found including a strong dependence of the tangent modulus on apparent density of the sheet, and a relative insensitivity of the tangent modulus to fiber length. The three stage behavior of the paper compression described by Rodal [Soft-nip calendering of paper and paperboard. Tappi Journal 72 (5), 177–186] was also accounted for in the model.