On the finite bending of functionally graded light-sensitive hydrogels Mohammad Shojaeifard . Mostafa Baghani Received: 28 December 2018 / Accepted: 31 May 2019 Ó Springer Nature B.V. 2019 Abstract Considering vast applications of light- sensitive hydrogels in designing sensors and actuators, in this article, a semi-analytical solution is developed for predicting the mechanical behavior of light- responsive hydrogels. Having continuous stress and deformation fields, the swelling of a functionally graded (FG) hydrogel strip is investigated under finite bending. Bending of FG hydrogel stems from the variation of cross-link density distribution along the thickness in the form of an exponential function which causes the layer to have an inhomogeneous swelling ratio. Furthermore, the finite element method is utilized to validate the accuracy of the presented solution by comparing the stress and deformation fields inside the light-sensitive FG hydrogel layer. A constitutive model for the light-sensitive hydrogels is modified in this paper to avoid multiple unstable so- lutions to arrive at a unique solution in various light intensities. Considering various applications of FG hydrogels, some designing factors are studied includ- ing the bending curvature, semi-angle, neutral axes and aspect ratio. In contrast to the layered structures, the swelling induced finite bending of an FG hydrogel gives continuous deformation and stress fields distributions. Keywords Light-sensitive hydrogel  Functionally graded strip  Semi-analytical solution  Finite bending  Finite element method 1 Introduction Hydrogels consist of sparse cross-link networks which have the capability of undergoing large deformation in response to various environmental stimuli. Being biocompatible, hydrogels have been employed widely in diverse applications. Considering the cross-link networks, hydrogels are capable of imbibing a vast amount of solvent to swell. Permeability is triggered by absorbing a fraction of water stems from the external stimuli, e.g., light [1–3], temperature [4–8], pH [9–11], electric [12], magnetic [13] and mechan- ical [14, 15] fields. Being responsive to the environ- mental conditions makes the smart hydrogels a potential candidate for vast applications through diffusing the solvent into the hydrogel network. The diffusion of solvent into the material domain is the key reason for the swelling mechanism which in recent years has been a hot topic in smart structures [7, 16, 17]. Smart hydrogels are studied in designing adaptive and smart structures including sensors and actuators [18], micro-valves [19, 20], drug delivery M. Shojaeifard  M. Baghani (&) School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran e-mail: baghani@ut.ac.ir M. Shojaeifard e-mail: m.shojaeifard@ut.ac.ir 123 Meccanica https://doi.org/10.1007/s11012-019-01004-4