Multiscale Method for Geometrical Nonlinear Analysis of Fluid Actuated Cellular Structures with Arbitrary Polygonal Microstructures

Fluid actuated cellular structures are morphing structures inspired by the nastic movement of plants. These materials have a wide array of applications from morphing aircraft wings to soft robotics. The nonlinear shape-morphing behaviors of the fluid actuated cellular structures composed of randomly distributed polygonal motor cells are investigated in this work. A new multiscale modeling framework based on multiscale finite-element methods is proposed to simulate the nonlinear behaviors of such adaptive materials with irregular polygonal microstructures. The multiscale displacement and hydraulic pressure base functions are firstly constructed to establish the relationship between the microstructures of the fluidic actuating cells and the macroscopic deformation on the polygonal coarse-scale mesh. Then, the corotational formulation for geometrically nonlinear analysis is integrated to this multiscale method to decompose the nonlinear deformations of the polygonal coarse-grid element into rigid-body motions and pure deformational displacements. In addition, a master-slave displacement relationship is employed to ensure the displacement continuity at the interface between the polygonal multiscale coarse-grid elements and the traditional fine-scale elements in a same computational model. Several representative examples including a smart wing structure are investigated to validate the accuracy and efficiency of the proposed polygonal multiscale corotational method.