Abstract
Compared with traditional linear elastic materials, the soft structure composed of incompressible hyperelastic materials has not only geometrical nonlinearity but also material nonlinearity during deformation. In this paper, the absolute nodal coordinate formulation (ANCF) is used to study the large deformations and large overall motions of incompressible hyperelastic curved beams. A novel large deformation dynamic modeling method for curved beams made of hyperelastic materials is proposed, in which a simplified Neo-Hookean model is combined with the one-dimensional ANCF beam element. The elastic force vector is calculated according to the exact expression of curvature. The dynamic equations are derived by using the virtual work principle. The dynamic responses of a cantilever silica gel beam under gravity are calculated based on the present method and compared with those of the improved low-order beam element (ILOBE), high-order beam element (HOBE), and commercial finite element analysis software (ANSYS). Simulation results show that the proposed method can accurately describe the large deformation and large overall motion of the beam, and has better computational efficiency. Research in this paper provides an efficient dynamic model for the dynamics analysis of soft robot arms.
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The datasets generated or analyzed during the current study are available from the corresponding author on reasonable request.
References
Wang, H.M., Zhu, Z.S., Jin, H., Wei, R., Bi, L., Zhang, W.L.: Magnetic soft robots: design, actuation, and function. J. Alloy. Compd. 922, 166219 (2022)
Shabana, A.A., Eldeeb, A.E.: Motion and shape control of soft robots and materials. Nonlinear Dyn. 104, 165–189 (2021)
Chen, Y.Z., Guo, X., Zhang, F.G., Li, L.: Dynamic modeling and analysis of rotating FG beams for capturing steady bending deformation. Appl. Math. Model. 88, 498–517 (2020)
Shabana, A.A.: An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies. Technical Report. no. MBS96–1-UIC (1996).
Shabana, A.A., Eldeeb, A.E.: Relative orientation constraints in the nonlinear large displacement analysis: application to soft materials. Nonlinear Dyn. 101, 2551–2575 (2020)
Shabana, A.A., Patel, M.: Locking alleviation in the large displacement analysis of beam elements: the strain split method. Acta Mech. 229, 2923–2946 (2018)
Sugiyama, H., Suda, Y.: A curved beam element in the analysis of flexible multi-body systems using the absolute nodal coordinates. Proceed Institution of Mech Eng, Part K: J Multi-body Dynam. 221(2), 219–231 (2007)
Otsuka, K., Makihara, K., Sugiyama, H.: Recent advances in the absolute nodal coordinate formulation: literature review from 2012 to 2020. J. Comput. Nonlinear Dyn. 17(8), 080803 (2022)
Zhang, P., Ma, J.M., Duan, M.L., Yuan, Y., Wang, J.J.: A high-precision curvature constrained Bernoulli-Euler planar beam element for geometrically nonlinear analysis. Appl. Math. Comput. 397, 125986 (2021)
Guo, X., Sun, J.Y., Li, L., Zhang, D.G., Chen, Y.Z.: Large deformations of piezoelectric laminated beams based on the absolute nodal coordinate formulation. Compos. Struct. 275, 114426 (2021)
Wu, J., Zhang, D.G., Li, L., Chen, Y.Z., Qian, Z.J.: Dynamic characteristics analysis of a rotating flexible curved beam with a concentrated mass. Chinese J Theoretical and Appl Mech. 51(4), 1134–1147 (2019)
Shabana, A.A., Desai, C.J., Grossi, E., Patel, M.: Generalization of the strain-split method and evaluation of the nonlinear ANCF finite elements. Acta Mech. 231, 1365–1376 (2020)
Hewlett, J., Arbatani, S., Kövecses, J.: A fast and stable first-order method for simulation of flexible beams and cables. Nonlinear Dyn. 99, 1211–1226 (2020)
Peng, X.F., Li, L.X.: State of the art of constitutive relations of hyperelastic materials. Chinese J Theoretical and Appl Mech. 52(5), 121–1232 (2020)
Melly, S.K., Liu, L.W., Liu, Y.J., Leng, J.S.: A review on material models for isotropic hyperelasticity. Int J Mech Syst Dynam. 1(1), 71–88 (2021)
Farzam, D.R., Shahab, S.: Large deformation analysis of fully incompressible hyperelastic curved beams. Appl. Math. Model. 93, 89–100 (2021)
Farzam, D.R., Nasser, F.: Large deformation analysis of two-dimensional visco-hyperelastic beams and frames. Arch. Appl. Mech. 91(10), 1–23 (2021)
Maqueda, L.G., Shabana, A.A.: Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams. Multibody Sys.Dyn. 18(3), 375–396 (2007)
Jung, S.P., Park, T.W., Chung, W.S.: Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law. Nonlinear Dyn. 63(1–2), 149–157 (2011)
Luo, K., Liu, C., Tian, Q., Hu, H.Y.: Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation. Nonlinear Dyn. 85, 949–971 (2016)
Orzechowski, G., Frączek, J.: Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF. Nonlinear Dyn. 82, 451–464 (2015)
Orzechowski, G., Frączek, J.: Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements. J. Theor. Appl. Mech. 55(3), 977–990 (2017)
Xu, Q.P., Liu, J.Y.: An improved dynamic model for a silicone material beam with large deformation. Acta. Mech. Sin. 34(4), 744–753 (2018)
Xu, Q.P., Liu, J.Y., Qu, L.Z.: Dynamic modeling for silicone beams using higher-order ANCF beam elements and experiment investigation. Multibody Sys.Dyn. 46(4), 307–328 (2019)
Greco, M., Peixoto, D.H.N.: Comparative assessments of strain measures for nonlinear analysis of truss structures at large deformations. Eng. Comput. 39(5), 1621–1641 (2022)
Hashiguchi, K.: Nonlinear continuum mechanics for finite elasticity-plasticity. Elsvier.151–162 (2020)
Buljak, V., Ranzi, G.: Constitutive Modeling of Engineering Materials. Academic Press. 83–105 (2021).
Melly, S.K., Liu, L.W., Liu, Y.J., Leng, J.S.: A review on material models for isotropic hyperelasticity. Int J Mech Syst Dynam. 1, 71–88 (2021)
Fernandes, L.W., Barbosa, G.B., Greco, M., Silveira, R.A.: Comparison between recent implicit time integration methods with frequency dissipation for nonlinear structural applications. Latin Am J Solids and Struct. 19(3), e441 (2022)
Bulín, R., Hajžman, M.: Efficient computational approaches for analysis of thin and flexible multibody structures. Nonlinear Dyn. 103, 2475–2492 (2021)
Funding
This research is supported by grants from the National Natural Science Foundation of China (Project Nos. 12072159 and 12232012) and the Fundamental Research Funds for the Central Universities (Project No. 30922010314).
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All authors contributed to the study conception and design. Formal analysis and investigation were performed by [Liang Li] and [Yaolun Wang]. Conceptualization by [Yongbin Guo]. Funding acquisition performed by [Liang Li] and [Dingguo Zhang]. The first draft of the manuscript was written by [Liang Li] and [Yaolun Wang] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Li, L., Wang, Y., Guo, Y. et al. Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation. Nonlinear Dyn 111, 4191–4204 (2023). https://doi.org/10.1007/s11071-022-08076-0
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DOI: https://doi.org/10.1007/s11071-022-08076-0