Meso-scale compaction simulation of multi-layer 2D textile reinforcements: A Kirchhoff-based large-strain non-linear elastic constitutive tow model

This paper presents a non-linear, large strain constitutive approach to modelling the mechanics of fibrous tows. The isotropic and linear St. Venant hyperelastic model was modified to extend its applicability to a transversely isotropic continuum. From this model, a set of large-strain material parameters which resemble the linear-elastic moduli was derived. The non-linear constitutive response of fibrous tows was accounted for through a modelling scheme that incorporates the instantaneous microstructural arrangement of the tows. Tow samples were isolated from the studied textile roll and subjected to a compression study utilising a custom-made tow compression rig, from which a set of material functions that fully defined the constitutive model were generated. The developed model was then implemented as a material subroutine and utilised in a mesoscopic compaction simulation of a multi-layer 2D woven reinforcement. It was found that the constitutive model performed very well in predicting the shape changes and stresses in deforming tows.