Identification of equivalent couple-stress continuum models for planar random fibrous media

Abstract

The purpose of this paper is to develop a homogeneous, couple-stress continuum model as a representation of 2D random fiber networks in the small deformation regime. The couple-stress substitution continuum is calibrated based on the response of a network model (window of analysis, WOA) subjected to prescribed kinematic boundary conditions applied on part of the WOA boundary, while the free surface boundary conditions are applied on complementary surfaces. Each fiber in the network is considered as a Timoshenko beam and the cross-links between fibers are modeled as welded joints in which the relative angles between the crossing beams remain constant during deformation, and hence they transmit moments along and between crossing fibers. The effective elastic constants of the couple-stress continuum are deduced by an equivalent strain energy method, and the characteristic lengths are identified from the resulting homogenized moduli. The competition between the affine (ADR) and non-affine (NADR) deformation regimes is shown to be quantified by the bending length, a scalar quantity that measures the relative importance of fiber bending in comparison with fiber stretch. The scaling laws of the effective moduli versus the bending length, network density and window size are determined in the affine and non-affine deformation regimes. The motivation of the adopted couple-stress substitution continuum is brought by comparing the identified effective non-classical properties with the mechanical properties predicted by FE simulations performed over the fully resolved fibrous network.