PneuNet, consists of a series of interconnected chambers embedded within a soft elastomer material, can exhibit diverse deformations. 3D printing allows for precise control over both material combinations and geometrical configurations, enabling the fabrication of PneuNets with complicated structures and multifunctionality. However, the increased freedom in material and structures introduced by 3D printing also presents significant challenges for modeling and design, including material nonlinearities, complex cross-sections and varying initial curvatures. In this work, we develop 3D-printed PneuNets with varying initial curvatures and cross-sections demonstrating finite deformation with multiple complete turns. To model the helical shape, we establish a general nonlinear framework based on the minimum potential energy method. The model is validated by PneuNets with various material combinations and geometrical configurations across a range of constitutive models including Mooney-Rivlin, Ogden, Neo-Hookean and Yeoh models. Results show that the nonlinear model, especially the Mooney–Rivlin model, accurately captures the deformation without any fitting parameters, achieving an$R^{2}$value of 0.975, compared to 0.017 for the linear model. Based on the validated model, PneuNets are inverse-designed to achieve desired spatial deformations. Their dynamic responses and payload capacities are also evaluated. We design a 3D-printed octopus with tentacles composed of PneuNets, capable of mimicking the grasping and movement of a real octopus. Additionally, we demonstrate the multifunctional capabilities such as fluid transition and sensing. This study lays a solid foundation for the design and application of 3D-printed PneuNets.

Lattice metamaterials exhibit diverse functions and complex spatial deformations by rational structural design. Here, lattice metamaterials are exploited to design pneumatic soft robots with programmable bending, twisting, and elongation deformations. The system comprises an elastomeric tube reinforced by lattice metamaterials. We develop an analytical framework to model the twisting, bending, and elongation finite deformation taking into account the geometric orthotropy and nonlinear elasticity. We experimentally validate our modeling approach and investigate the effects of geometric patterns and input loading on the soft actuators' deformation. Theoretical guided design of lateral-climbing soft robots and exploration soft manipulators are demonstrated. The soft actuator could exhibit a combined twisting–bending–elongation deformation by lattice superimposition. The proposed structural design method paves the way for designing soft robots with complex and dexterous deformations.