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

Abstract

In this work, we study the growth-induced bending deformations of multi-layered hyperelastic plates. First, under the assumption of plane strain, we formulate the 3D governing system for a multi-layered hyperelastic (neo-Hookean) plate, which incorporates the growth parameters in the different layers. Based on the governing system and by adopting a series expansion–truncation approach, we derive a plate equation system. In the case of traction-free boundary conditions, we solve the plate equation system explicitly and obtain some simple analytical results, which can be used to describe the deformations of the multi-layered plates induced by growth. We verify the accuracy and efficiency of the analytical results through comparisons with some numerical and experimental results. We also provide a comparison between the analytical results obtained for single- and multi-layered hyperelastic plates. Furthermore, we analyze the properties of residual stresses in the multi-layered plates. The plate equation system and the analytical results obtained here have wide potential applications in the design of intelligent soft devices.