A Non-Orthogonal Constitutive Material Model for Advanced Woven Fabrics Based on a Mesoscale Unit Cell

Abstract

Advanced woven fabrics can provide a wide range of mechanical properties since the yarns can be arranged in different architectural patterns thus allowing the fabric structure to be tuned based on the specific needs. This adjustable nature makes them an attractive material choice for applications where versatility is highly desired. Hence, there is an increasing interest in woven fabrics in the recent years. They have been used in various applications such as deployable structures, protective garments, medical scaffolds and composites. With the increased interest, there is a need for efficient and accurate computational tools to investigate the mechanical behavior and deformation of woven fabrics for specific applications. Although there are several computational models in the literature that can model uniaxial and biaxial behavior of woven fabrics, there are not any commonly accepted material models for woven fabrics due to the complex interaction of trellising and deformation. Here, we propose an easy to implement constitutive material model based on a mesoscale unit cell of the woven fabrics. The proposed model utilizes the two prominent deformation mechanisms affecting the mechanical response at the mesoscale level: (1) Yarn stretching, and (2) shearing. These mesoscale mechanisms are mechanistically implemented within an unit cell by using truss and rotational springs to generate the mechanical response of the woven fabric. The yarns’ nonlinear mechanical behavior is modeled with non-linear trusses and assumed to be pin-jointed at the center of the unit cell. The truss elements are allowed to rotate at the pin-joint reproducing the yarns’ relative rotational motion during shearing. The fabric’s shear resistance involves two components: yarn-to-yarn relative rotation/sliding and yarn locking due to the yarn transverse compression. These components of the fabric shear resistance are modeled as a non-linear rotational spring located at the pin-joint which generates a moment resisting the shear deformation. The developed forces and moments from the trusses and rotational spring within the unit cell structure are then used to determine the continuum stress state of the material point. The material properties and parameters defined in the proposed model are easy to obtain from uniaxial tensile and shear tests on fabrics. To validate the material model, plain weave Kevlar KM2 fabric is modeled by replicating the standard uniaxial tensile and bias extension tests. The results obtained show that the material model provides a good description of the in-plane deformation and mechanical response.