A continuum model based on Rayleigh dissipation functions to describe a Coulomb-type constitutive law for internal friction in woven fabrics

A continuum model intended to provide predictions for the response of a woven fabric that includes the effects of friction between fibers is proposed. Specifically, we consider a macroscopic formulation in which the fabric weave is composed of two orthogonal families of continuously distributed yarns. The elastic behavior of the planar fabric is characterized by a second-gradient formulation, incorporating the capacity of the fibers to resist a bending deformation. Particular care is devoted to modeling the action of preventing fiber overlapping through a potential energy barrier. The frictional sliding effect of warp threads interwoven with the weft yarns is introduced through a Rayleigh dissipative function that can be appropriately shaped to consider a Coulomb-type law. Spinning friction of yarns belonging to different families also is conceived when a relative rotation between fibers is present to generalize the dissipation phenomenon involved in the considered sheet. Numerical simulations of the proposed model are provided and discussed.