Large Bending Deformation of a Cantilevered Soft Beam under External Load: The Applicability of Inextensibility Assumption of the Centerline

Background: Soft materials, including elastomers and gels, are pervasive in biological systems and technological applications. Despite the rapid developments of soft materials in the recent decades, it is still challenging to theoretically model and predict the large-deformation behaviors of soft structures. Objective: The goal of this work is to give a general theoretical model to investigate the large deformation of a cantilevered soft beam under various loads. In particular, the applicability of the inextensibility assumption of the beam centerline is explored. Methods: The governing equations of the soft beam system are derived according to the principle of minimum potential energy. In order to investigate the large deformation of the soft beam, the curvature of the beam centerline is exactly considered and the Yeoh model is utilized to account for the hyperelasticity of the soft beam. The derived ordinary differential equations are discretized by the Galerkin method and then solved by the iterative algorithm. Results: Based on the proposed theoretical model, large bending deformations of the cantilevered soft beam are analyzed for various types of external loads, including uniformly distributed force, tipend concentrated force, and non-uniformly distributed force. Different values of the amplitude of the external loads are considered and fruitful deformed configurations are presented. Conclusion: The proposed model is able to study the large deformation of the soft beam effectively. The inextensibility assumption of the beam centerline is applicable when the amplitude of the external load is relatively small. When the amplitude of the external load is sufficiently large, the extension of the centerline needs to be considered.