4D textiles are a specific class of 4D printed systems obtained by 3D printing on elastically pre-tensioned textiles, enabling the realization of 3D objects from 2D patterns, upon a self-shaping process when the fabric tension is released, or, as some studies suggest, by remote actuation via temperature change. Tipically, curved shapes are obtained, with curvatures that stem from a complex biaxial stress state due to the confinement of rigid/semi-rigid printed elements on the stretched textile.

This study examines the relationship between textile pre-stretch (Lycra; modulus ∼ 1MPa), printed element stiffness, and resulting curvature in both simple and complex geometries (bars on monoaxially stretched textiles; single/multiple star-shaped patterns on biaxially stretched textiles). The stiffness of the printed elements was controlled by varying their thickness and the material Young’s modulus. The parameters were varied to explore a range of curvatures, from degenerate flat configurations, through regular curvatures to multi-stable buckling.

The strain evolution during shape transformation was analyzed using a stereoscopic digital image correlation (DIC) system, which helped to explore the relationship between the strain field and the 4D textiles' structural and kinematic behaviour. A finite element model was created, calibrating it on the specific properties of the various materials, to simulate the whole 4D textile history, from textile stretching, upon establishment of a contact between printed elements and textile, and finally at the release of the stress. Validation, carried out by comparing FE results with those emerging from DIC, show that the model was capable of accurately reproducing the behavior of 4D textiles, especially regarding the shape and the displacement of the curved elements and the occurrence of multi-stability, although emerged discrepancies suggest the need for more complex models.