Bias extension test on an unbalanced woven composite reinforcement: Experiments and modeling via a second-gradient continuum approach

TL;DR

This paper introduces a second-gradient continuum model to better describe the complex deformation behaviors of unbalanced woven composites during bias extension tests, capturing microstructural effects and asymmetric deformation patterns.

Contribution

A novel second-gradient hyperelastic model for unbalanced woven fabrics that incorporates microstructural effects like yarn bending stiffness and relative sliding.

Findings

Model accurately reproduces experimental asymmetric S-shaped deformation.

Captures microstructural deformation patterns at the mesoscopic scale.

Demonstrates improved prediction over classical continuum models.

Abstract

The classical continuum models used for the woven fabrics do not fully describe the whole set of phenomena that occur during the testing of those materials. This incompleteness is partially due to the absence of energy terms related to some micro-structural properties of the fabric and, in particular, to the bending stiffness of the yarns. To account for the most fundamental microstructure-related deformation mechanisms occurring in unbalanced interlocks, a second-gradient, hyperelastic, initially orthotropic continuum model is proposed. A constitutive expression for the strain energy density is introduced to account for i) in-plane shear deformations, ii) highly different bending stiffnesses in the warp and weft directions and iii) fictive elongations in the warp and weft directions which eventually describe the relative sliding of the yarns. Numerical simulations which are able to reproduce the experimental behavior of unbalanced carbon interlocks subjected to a Bias Extension Test are presented. In particular, the proposed model captures the macroscopic asymmetric S-shaped deformation of the specimen, as well as the main features of the associated deformation patterns of the yarns at the mesoscopic scale.