Nonlinear Elasticity of Fiber Masses
Doctoral thesis, 2002
The mechanical properties of fiber masses are important in many fields of engineering such as upholstery, paper making, and composite manufacturing, and a fair amount of work has gone into analyzing these properties. However, previous theories have been limited to simple deformations and a restrictive choice of deformation mechanism. Another obstacle has been to perform experiments in other than simple deformations.
This dissertation is concerned with the elastic response of a mass of entangled and crimped fibers when subjected to large deformations. The work embraces the experimental as well as the theoretical problems involved. An experimental technique is developed for the careful measurement of stress-strain relations. Compared to previous techniques the main benefits are triaxiality, elimination of edge effects and suitability for anisotropic materials. The novel apparatus is thoroughly validated, both analytically and experimentally.
A micromechanical theory for the modeling of flexible granular solids based on affine average motion of inter-particle contacts is presented. Based on this theory, we develop two different models that differ in the choice of convected force rate of the contact forces between fibers. The first model is simplest and works well for deformations that are predominantly compressive. The second model is more general, but leads to a more complex description involving three partial stresses with a separate constitutive equation for each. Unlike earlier models these are properly material frame-indifferent, and use a more refined description of the contact deformation mechanisms. The first model is also extended to allow for a distribution of fiber diameters.
Experiments were performed using the aforementioned technique, using samples of carded PA-6 fibers. The first model is validated against uniaxial compression tests (both monodisperse and polydisperse fiber diameters) and the second against uniaxial compression, isochoric shear and simultaneous compression and shear. The theoretical predictions are found to be in excellent agreement with the experimental data.