A shearable and thickness stretchable finite strain beam model for soft structures

He, L, Lou, J, Dong, Y, Kitipornchai, S and Yang, J 2018, 'A shearable and thickness stretchable finite strain beam model for soft structures', Meccanica, vol. 53, no. 15, pp. 3759-3777.


Document type: Journal Article
Collection: Journal Articles

Title A shearable and thickness stretchable finite strain beam model for soft structures
Author(s) He, L
Lou, J
Dong, Y
Kitipornchai, S
Yang, J
Year 2018
Journal name Meccanica
Volume number 53
Issue number 15
Start page 3759
End page 3777
Total pages 19
Publisher Springer Netherlands
Abstract Soft materials and structures have recently attracted lots of research interests as they provide paramount potential applications in diverse fields including soft robotics, wearable devices, stretchable electronics and biomedical engineering. In a previous work, an Euler�Bernoulli finite strain beam model with thickness stretching effect was proposed for soft thin structures subject to stiff constraint in the width direction. By extending that model to account for the transverse shear effect, a Timoshenko-type finite strain beam model within the plane-strain context is developed in the present work. With some kinematic hypotheses, the finite deformation of the beam is analyzed, constitutive equations are deduced from the theory of finite elasticity, and by employing the standard variational method, the equilibrium equations and associated boundary conditions are derived. In the limit of infinitesimal strain, the new model degenerates to the classical extensible and shearable elastica model. The corresponding incremental equilibrium equations and associated boundary conditions are also obtained. Based on the new beam model, analytical solutions are given for simple deformation modes, including uniaxial tension, simple shear, pure bending, and buckling under an axial load. Furthermore, numerical solution procedures and results are presented for cantilevered beams and simply supported beams with immovable ends. The results are also compared with the previously developed finite strain Euler�Bernoulli beam model to demonstrate the significance of transverse shear effect for soft beams with a small length-to-thickness ratio. The developed beam model will contribute to the design and analysis of soft robots and soft devices.
Subject Solid Mechanics
Keyword(s) Bending-to-stretching transition
Finite strain
Hyperelastic
Shearable
Soft materials
DOI - identifier 10.1007/s11012-018-0905-4
Copyright notice © Springer Nature B.V. 2018
ISSN 0025-6455
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