A viscoelastic model for the compaction of fibrous materials

Fibrous materials experience compression in many important industrial and technical applications. They are known to undergo a viscoelastic response in such circumstances, exhibiting phenomena such as dependence on compaction velocity, stress relaxation and stress-strain hysteresis. In this paper, a model has been developed for the stress in compacting fibrous materials. The model is based on the multiplicative decomposition of the stress into a function of the strain and a second function of the strain-rate. The model is applicable to that class of materials whose stress-strain responses at different compaction velocities can be collapsed onto a single master curve when the stress is normalised appropriately. The model parameters can be determined using a least-squares fitting to a select number of test data. The model has been tested for two materials of different architectures over a range of compaction speeds and maximum volume fractions; the match to experimental data is excellent.