Analytical study on growth-induced bending deformations of multi-layered hyperelastic plates. (March 2020)

• Record Type: Journal Article
• Authors: Du, Ping; Dai, Hui-Hui; Wang, Jiong; Wang, Qiongyu
• Is Part Of: International journal of non-linear mechanics. Volume 119(2020)
• Publication Date: 2020-03
• Subjects: Multi-layered hyperelastic plate -- Growth deformation -- Plate theory -- Analytical solution; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.103370
• Languages: English
• ISSNs: 0020-7462

Abstract

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. Highlights: The growth-induced bending deformation of a multi-layered hyperelastic plate is studied. A plate equation system for multi-layered hyperelastic plates is derived. Under traction-free boundary conditions, some explicit analytical results are obtained. The analytical results can fit the numerical and experimental results quite well. The properties of residual stresses in multi-layered hyperelastic plates are analyzed.