Open AccessLarge Bending Deformation of a Cantilevered Soft Beam under External Load: The Applicability of Inextensibility Assumption of the Centerline
Author(s) -
Wei Chen,
Lin Wang
Publication year - 2021
Publication title -
current mechanics and advanced materials
Language(s) - English
Resource type - Journals
eISSN - 2666-1853
pISSN - 2666-1845
DOI - 10.2174/2666184501999200909151326
Subject(s) - hyperelastic material , beam (structure) , cantilever , bending , deformation (meteorology) , discretization , curvature , galerkin method , bending stiffness , timoshenko beam theory , mechanics , computer science , structural engineering , physics , mathematics , mathematical analysis , finite element method , geometry , engineering , meteorology
Background: Soft materials, including elastomers and gels, are pervasive in biologicalsystems and technological applications. Despite the rapid developments of soft materials in the recentdecades, it is still challenging to theoretically model and predict the large-deformation behaviors ofsoft structures. Objective: The goal of this work is to give a general theoretical model to investigate the large deformationof a cantilevered soft beam under various loads. In particular, the applicability of the inextensibilityassumption of the beam centerline is explored. Methods: The governing equations of the soft beam system are derived according to the principle ofminimum potential energy. In order to investigate the large deformation of the soft beam, the curvatureof the beam centerline is exactly considered and the Yeoh model is utilized to account for thehyperelasticity of the soft beam. The derived ordinary differential equations are discretized by theGalerkin method and then solved by the iterative algorithm. Results: Based on the proposed theoretical model, large bending deformations of the cantileveredsoft beam are analyzed for various types of external loads, including uniformly distributed force, tipendconcentrated force, and non-uniformly distributed force. Different values of the amplitude of theexternal 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 externalload is relatively small. When the amplitude of the external load is sufficiently large, the extensionof the centerline needs to be considered.