Modelling of curled fibres in two-dimensional networks

A two-dimensional micromechanical model for fibre networks constructed of curled fibres is presented. In the model, which allows for a general statistical description of parameters such as fibre length, fibre orientation and curl factors, the fibres are modelled as circle segments. By varying the radius of the circle anything from almost straight to half circle shaped fibres can be modelled. The mechanical response of the network model is obtained by finite element analysis. The fibres are modelled with beam elements having linear elastic material properties and a cross sectional area corresponding to that of an idealized circular fibre. The model is used to investigate the influence of fibre curl, fibre length and percentage of bonded fibre crossings on the mechanical behaviour of paper sheets of low to medium basis weight. The tensile stiffness index for different fibre curl is qualitatively compared with experimental data. The results from the present model show a less pronounced influence of the fibre curl compared to the experimental data and several possible reasons for this discrepancy are discussed. Large deformation analyses allowing for applied strains up to 5% results in a non-linear relation between the tensile stiffness index and the strain for curled fibres. For straight fibres the non-linear relation is less pronounced, although the difference is small. This result indicates that the ability of the fibre to carry load depends on the curl factor.