An enhanced kinematic forming framework for fast and accurate prediction of in-plane strains in unidirectional fabrics

Unidirectional (UD) fabrics are attractive for high-performance structures due to their high stiffness-to-weight ratio. However, realising these benefits in components with curved geometries requires accurate prediction of forming behaviour to control manufacturing-induced defects and obtain reliable fibre orientations for structural analysis. Existing finite element forming models capture relevant deformation mechanisms but are computationally expensive, limiting applicability in large-scale optimisation and parametric design studies increasingly required in industrial development cycles. Kinematic forming models offer a computationally efficient alternative, but existing approaches are largely limited to pure-shear assumptions that are unsuitable for UD fabrics, while simple-shear formulations have received limited attention and algorithmic development and generally cannot represent transverse deformation. To address these limitations, this paper presents a kinematic forming framework based on simple-shear kinematics with an experimentally calibrated shear-dependent fibre spacing. The framework employs robust geometric intersection algorithms to construct fibre paths on single-valued surfaces and introduces a new enhanced simple-shear model capable of representing both shear and deformation perpendicular to fibres in UD non-crimp fabrics (UD-NCFs). The simple-shear formulation is verified against analytical hemispherical forming solutions, while the enhanced simple-shear model is calibrated using a 0° UD-NCF forming case and validated against a 45° UD-NCF forming case through comparison with experiments and high-fidelity finite element simulations. The proposed framework accurately predicts deformed geometry and geometrically-derived in-plane strain fields while achieving speed-up factors of 134-251 compared with finite element simulations. The kinematic framework is therefore well suited for optimisation and early-stage design studies. The software implementation is freely available at https://doi.org/10.5281/zenodo.22044780.