Analytical study on growth-induced bending deformations of multi-layered hyperelastic plates

Abstract In this work, a novel analytical approach is proposed to study the growth-induced bending deformations of multi-layered hyperelastic plates. First, under the assumption of plane strain, the 3D governing system for a multi-layered hyperelastic (neo-Hookean) plate is formulated, which incorporates the growth parameters in the different layers. Based on the governing system and by adopting a series expansion-truncation approach, a plate equation system can be derived. In case of traction-free boundary conditions, the plate equation system are solved explicitly and some simple analytical results are obtained, which can be used to describe the deformations of the multi-layered plates induced by growth. The accuracy and efficiency of the analytical results are verified through the comparisons with some numerical and experimental results. The comparison between the analytical results obtained for single- and multi-layered hyperelastic plates has also been given. Furthermore, the properties of residual stresses in the multi-layered plates are analyzed. The plate equation system and the analytical results obtained in the current work have wide potential applications in the design of intelligent soft devices.