A NEW APPROACH TO THE THEORY OF THE COMPRESSION OF FIBER ASSEMBLIES

A formula is presented for the mechanics of a fiber mass under extensive compression. The mass is treated as the assembly of the fiber elements whose individual bending behaviors are combined into the overall response of the mass. The stress-strain relation and Poisson's ratio are expressed in terms of the strain-dependent density of fiber orientation, the spatial density of fiber length, and the properties of fibers. The theory differs from others proposed in three respects: the length of the bending element depends on the respective orientation, the law to describe the change in the direction distribution induced by compression is given in a differential form, and the mechanical relation is derived by the energy method. The general theory is applied to three special cases for a random mass; in the case of isotropic compression, an analytical solution equivalent to van Wyk's is derived; in two cases of uniaxial compression, with and without lateral confinement, numerical calculation predicts, respectively, stress and strain induced in the transverse direction.