Preliminary Modeling of Single Pulp Fiber Using an Improved Mass–Spring Method

An improved Mass–Spring Model (iMSM) is developed by adding central springs to the conventional Mass–Spring Models (MSMs) of tubular structures. This improvement is necessary to model fibers that have enough stiffness so that they do not collapse under transverse loading. Such is the case with many pulp fibers used in papermaking. Four different types of pulp fibers (Aspen CTMP, Aspen BCTMP, Birch BCTMP, and Spruce BKP) were simulated in the study. A geometric model and iMSM of a single fiber were developed, in which the topological structure of iMSM is explained in detail. The mass of mass points and the elastic coefficient of different springs in iMSM were calculated using axial tensile and torsional responses. A dynamic simulation of transverse bending of the fiber over a rigid cylinder and subjected to a transverse pressure was used to determine the effective elastic modulus for four different single fibers and compared to experimental values with an average relative error of 8.49%. The dynamic simulations were completed in 1.04–2.64 min for the four different paper fibers representing sufficient speeds to meet the needs of most real application scenarios. The acceptable accuracy and the fast simulation speed with the developed iMSM fiber model demonstrate the feasibility of the methodology in analyzing paper structures as well as similar fiber-based materials.