Curvature-Programmable Sheet-to-3D Morphing of Single-Material Architected Laminates: A Functionally Graded Framework for Foaming-Induced Bending

Abstract

Curvature-programmable sheet-to-three-dimensional (3D) morphing with a single principal curvature is demonstrated in single-material polylactic acid (PLA) laminates through the combined use of fused deposition modeling (FDM) and solid-state microcellular foaming, without requiring multi-material architecture or stimulus-responsive additives. The foaming process generates a surface-to-core gradient in cellular morphology driven by through-thickness thermal asymmetry during CO2-induced cell nucleation and growth, producing spatially graded stiffness and anisotropic free-expansion strain across the laminate thickness. This material-level heterogeneity, coupled with raster-direction orthotropy inherited from the printed filament architecture, creates a built-in eigenstrain mismatch that drives programmable bending upon foaming. Asymmetric allocation of upper and lower printed layers constitutes the primary design handle for curvature control, while printing speed modulates chain orientation and provides secondary fine-tuning of the expansion anisotropy. A functionally graded laminate model integrating classical laminated plate theory with experimentally calibrated gradation parameters quantitatively reproduces the curvature response (R2 = 0.9216) and supports an inverse design procedure for target shape realization. The foamed cellular architecture further yields an 8.2% increase in specific energy absorption under compression. Unlike prior systems that rely on multi-material assembly, stimulus-responsive additives, or extrinsic surface patterning, this approach programs a continuous, model-predicted curvature in a single polymer through an intrinsic through-thickness gradient with an inverse design procedure. This work establishes a single-polymer, additive-manufacturing-compatible platform in which microstructural gradients serve as programmable material descriptors for lightweight morphing structures.