Modeling and computer simulation of the compression and recovery behavior of fiber assemblies

The behavior of fiber assemblies under compression and after the release of the compressive force is an important problem in the textile industry. It has been studied mathematically for over 50 years. Applications of this work include predicting the properties of wool or fiber fill based on the fibers and processing used, designing insulation that retains its insulating properties after being compressed, and developing materials for noise and vibration control.; Here a mathematical model is derived that describes the three dimensional behavior of individual fibers. The model is based on the Love-Kirchhoff equations for a long, thin, naturally curved rod. The compressional behavior of an ensemble of these fibers within a unit cell is calculated by solving the equations of equilibrium at a large number of successive steps, which provides a prediction of the forces between the fibers. The model takes into account both static and kinetic friction. Unlike previous models, this model is not based on the assumed behavior of idealized bending elements.; Computer simulations are run for four cases with two different friction conditions in order to compare predictions of this model with experimental results and with van Wyk's theory of the uniaxial compression of an initially random fiber assembly. These simulations are the first to show a reasonable ability to predict the undetermined constant K in van Wyk's equation. They also show a significantly greater number of fiber-fiber contacts being formed than theories based only on the diameter and arrangement of fibers have predicted. The predicted contacts have a wide range of contact forces while only a small percentage of them do not slip.; Simulations of compression-release cycling are able to produce realistic looking hysteresis plots, and can predict the amount of frictional energy dissipated as a function of time. It is not found that irrecoverable compression increases for as many cycles as has been experimentally reported, which may be a result of neglect of viscoelastic effects. It is found that fiber crimp has a large effect on the compressional properties of an assembly in that more highly crimped fibers absorb more energy as they are compressed. They also absorb a higher proportion of their energy in the twisting mode, which has been neglected by previous investigators. A lower induced orientation effect than that predicted by Stearn's theory is found, but lack of experimental data currently prevents resolution of this discrepancy.; Suggestions for future work include improving the performance of the computer program so that it may handle larger simulations, incorporating viscoelastic effects and an improved friction model into the fiber model, and developing a means to predict the most probable initial geometry of an assembly from the properties of its component fibers.