Automated model discovery for textile structures: The unique mechanical signature of warp knitted fabrics

Textile fabrics have unique mechanical properties, which make them ideal candidates for many engineering and medical applications: They are initially flexible, nonlinearly stiffening, and ultra-anisotropic. Various studies have characterized the response of textile structures to mechanical loading; yet, our understanding of their exceptional properties and functions remains incomplete. Here we integrate biaxial testing and constitutive neural networks to automatically discover the best model and parameters to characterize warp knitted polypropylene fabrics. We use experiments from different mounting orientations, and discover interpretable anisotropic models that perform well during both training and testing. Our study shows that constitutive models for warp knitted fabrics are highly sensitive to an accurate representation of the textile microstructure, and that models with three microstructural directions outperform classical orthotropic models with only two in-plane directions. Strikingly, out of 2${}^{14}=$16,384 possible combinations of terms, we consistently discover models with two exponential linear fourth invariant terms that inherently capture the initial flexibility of the virgin mesh and the pronounced nonlinear stiffening as the loops of the mesh tighten. We anticipate that the tools we have developed and prototyped here will generalize naturally to other textile fabrics–woven or knitted, weft knit or warp knit, polymeric or metallic–and, ultimately, will enable the robust discovery of anisotropic constitutive models for a wide variety of textile structures. Beyond discovering constitutive models, we envision to exploit automated model discovery as a novel strategy for the generative material design of wearable devices, stretchable electronics, and smart fabrics, as programmable textile metamaterials with tunable properties and functions. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

Statement of significance

Textile structures are rapidly gaining popularity in many biomedical applications including tissue engineering, wound healing, and surgical repair. A precise understanding of their unique mechanical properties is critical to tailor them to their specific functions. Here we integrate mechanical testing and machine learning to automatically discover the best models for knitted polypropylene fabrics. We show that warp knitted fabrics possess a complex symmetry with three distinct microstructural directions. Along these, the behavior is dominated by an exponential linear term that characterize the initial flexibility of the virgin mesh and the nonlinear stiffening as the loops of the fabric tighten. We expect that our technology will generalize naturally to other fabrics and enable the robust discovery of complex anisotropic models for a wide variety of textile structures.