Geometrical and regression-based modeling of shell-like deformations in pneumatically actuated thermoplastic fiber-reinforced hybrid composites

Abstract Adaptive structures capable of controlled shape change are increasingly demanded in fields such as aerospace, architecture, and automotive engineering. In these applications, shell-like deformations are essential for achieving smooth surface transitions that satisfy aesthetic requirements or improve aerodynamic performance. While pressure-actuated cellular structures (PACS) and bio-inspired designs have demonstrated promising morphing capabilities, they often involve high geometric complexity, rely on antagonistic actuation systems requiring energy input in both directions of motion, or face limitations in manufacturability. Inspired by biological systems such as insect wings, this study presents a novel approach to implement shell-like deformations in planar, mold-free manufacturable, thermoplastic fiber-reinforced hybrid composites using embedded pneumatic actuators which are integrated into pre-formed cavities within the laminate setup. Previous implementations have been limited to uniaxial bending deformations. In contrast, the integration of multiple actuators enables shell-like deformations through coupled bending axes. Unlike antagonistic systems, the elastic stiffness of the fiber-reinforced composite serves as a passive restoring force, allowing for reversible deformation without additional counteractuation or mechanical complexity. In this study, a simplified geometric model combined with a regression-based approach is developed to predict deformation as a function of actuation pressure p , actuator width w , and the spacing d between coupled actuators and thereby eliminate the need for computationally intensive FEM simulations. The model is validated within the tested range of p (0.0 to 1.8 bar), w (20 to 50 mm) and d (10 to 40 mm): bending angles of up to 92 $$^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> </mml:math> and corresponding shell radii as small as 50 mm were reproducibly achieved, with a coefficient of determination of $${R}^{{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> = 0.96 for $${w = }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>w</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 20 mm, for example. The proposed design strategy bridges the gap between biologically inspired compliant mechanisms and scalable technical implementation of adaptive shell-like components, offering a low-complexity solution based on a planar, mold-free manufacturing approach.