Mechanical modelling of twisted yarns
Understanding fibre interactions and variability in yarn tensile behaviour
We develop mechanical models of twisted yarns to understand how fibre arrangement, friction and differences in fibre properties influence their tensile behaviour. Our virtual fibre approach reproduces key features of the measured cotton and wool yarn responses and reveals how fibres share load as the yarn deforms and individual fibres fail.
Twist gives yarns their cohesion, but their mechanical response depends on more than the twist level alone. Fibres follow different paths, reorient during loading and transfer forces through contact and friction. Differences in fibre stiffness and strength affect how the load is shared and how failure develops. Representing these interacting mechanisms remains a challenge for predictive yarn models.
Mechanical models complement experimental testing and manufacturing experience by allowing selected material and structural parameters to be varied systematically. They help connect the behaviour of individual fibres to the stiffness, strength and deformation of the yarn as a whole.
Representing the twisted fibre structure
Our approach generates an idealised yarn geometry from information about its cross-section and twist. A reduced number of interacting virtual fibres represents the real fibre population, keeping the simulations manageable. The model accounts separately for resistance to stretching and bending, while contact and friction transfer forces between neighbouring fibres as the yarn deforms. The model allows fibre properties to vary while keeping the yarn geometry unchanged. This makes it possible to examine how property variability and its distribution among fibres affect the yarn response.
Comparison with cotton and wool yarns
We compared the simulations with tensile experiments on cotton and wool yarns. The model captured key features of their contrasting responses, including the initial stiffness and the transition to a more compliant response in wool. For cotton, the simulations also included fibre failure and reproduced the response up to the main loss of load-carrying capacity. Field variables represent fibre-to-fibre differences by scaling the stiffness and tensile strength of each virtual fibre. Each factor remains constant along that fibre. With identical mean properties, the more aligned core fibres carry a larger share of the axial load. Introducing property scatter spreads load and damage more widely across the yarn, changing how failure develops (Figure 3).
Field variables allow the model to resolve how differences in fibre stiffness and strength govern local load sharing. Fibres reach their failure conditions at different stages, making the transfer of load from a broken fibre to its surviving neighbours visible. The mean field model assigns identical properties to all fibres and cannot capture this variability-driven pattern of load redistribution, with failure developing in a more concentrated sequence. Figure 4 illustrates the local mechanism: stress falls near the broken ends, increases in neighbouring fibres and recovers along the broken fibre through frictional contact. This redistribution allows isolated fibre breaks without an immediate loss of overall yarn load.
A contribution to broader textile modelling
The present model uses idealised continuous helical fibres. It does not explicitly represent finite staple-fibre ends, fibre migration or detailed fibre pullout after failure. Its agreement with the tested yarn responses supports its use within the investigated scope, while these local mechanisms require further development.
Within that scope, the framework provides a basis for investigating how twist and variability in fibre properties affect yarn performance. Developed alongside experimental characterisation, it contributes to textile models that connect fibre-scale mechanisms to the behaviour of larger fibrous structures.
Further information
Acknowledgments
Supported by FWO fundamental research project G059425N, Ghent University projects bof/baf/1y/2025/01/003 and BOF/STA/202009/046, and the ICON project SIM3TEX (HBC.2022.0788).
Contact
Prof. dr. ir. Lode Daelemans (Lode.Daelemans@UGent.be)