Line-based 4D-printed thermoplastics enabled by layerwise printing speed control: Concept, mechanics, and inverse design

Thermally induced shrinkage in fused deposition modelling (FDM) of semi-crystalline thermoplastics is conventionally regarded as a manufacturing defect that compromises dimensional accuracy. In this work, we demonstrate that printing-induced shrinkage can instead be deliberately harnessed as a programmable design variable for deterministic shape forming. A co-directional, single-material printing strategy is proposed in which layerwise modulation of printing speed is used to control crystallinity development and, consequently, through-thickness shrinkage gradients. Upon thermal activation, these gradients generate predictable bending moments that transform initially straight, planar line elements into prescribed three-dimensional geometries. A systematic experimental programme is conducted to establish quantitative process–structure–property relationships linking printing speed, shrinkage strain, and resulting curvature. Building on this database, a reduced-order analytical model based on multi-layer beam theory is developed to predict the thermally activated deformation of isolated line elements and is validated through finite element simulations and experiments. Using this forward model, a mechanics-guided inverse design framework is formulated to map target geometries directly to layerwise printing speed distributions, enabling automated generation of manufacturing-ready process parameters. When extending the approach to continuous architectures fabricated via uninterrupted filament deposition, non-local thermal interactions are identified, leading to systematic curvature under-actuation and deviation from isolated-element predictions. To address this limitation, an iterative geometric calibration strategy is introduced and integrated into the inverse design workflow, enabling high-fidelity reconstruction of complex shapes. The framework is validated experimentally through a series of demonstrations, including alphabetical and non-trivial planar geometries. Overall, this study establishes layerwise crystallinity control via printing speed modulation as a manufacturing-compatible route for programmable shape forming in thermoplastic additive manufacturing, offering a scalable alternative to multi-material printing and complex toolpath anisotropy for 4D-printed structures. • Single-material, uni-directional printing enables 4D shape forming. • Layerwise speed control programs shrinkage for deterministic shape forming. • Experiments map print speed to shrinkage strain and curvature quantitatively. • A reduced-order multilayer beam model predicts thermally activated bending. • Inverse design plus geometric calibration enables accurate complex-shape forming.