Geometrically exact 3D arbitrarily curved rod theory for dynamic analysis: Application to predicting the motion of hard-magnetic soft robotic arm

Li，Xin; Yu，Wenkai; Zhu，Xiaoyan; Liu，Ju; Yuan，Hongyan

2024-10-01

10.1016/j.apm.2024.05.044

Applied Mathematical Modelling   影响因子和分区

0307-904X

Magnetorheological elastomers are active materials which can be actuated by the applied magnetic field. Hard magnetic soft (HMS) materials, a type of magnetorheological elastomers, show great potential in the fields of biomedical engineering and soft robotics, due to their short response time, remote operation, and shape programmability. To exploit its potential, a series of theoretical frameworks of HMS rods have been developed, but they are mainly limited to the static rod models or classical curved rod models that fail to consider the effect of the “initial curvature” on the distribution of the stress. In this work, we develop a curved rod theory to predict the 3D dynamic motion of the rod-like HMS robotics under large deformation. Based on the geometrically exact rod theory, we include the heterogeneous initial length of the longitudinal fiber caused by “initial curvature” into our model and obtain the reduced balance equations of the HMS robotics. As a result, the “tension-bending” and “shear-torsion” coupling effects of curved rods emerge in the present model. A numerical implementation of our model based on the classical Newmark algorithm is presented. To validate our model, three numerical examples, including the dynamic snap-through behavior of a bistable arch, are performed and compared with the simulation or experiment results reported in literatures, which show a good agreement. Finally, we experimentally study the 2D and 3D static and dynamic motion of a quarter arc HMS robotic arm under an applied magnetic field of 10 mT, and our model gives a satisfactory prediction, especially for static deformation.

3D large deformation Dynamic analysis Finite element method Geometrically exact curved rod Hard-magnetic soft robotics Magnetorheological elastomers

SCI ; EI

英语

第一 ; 通讯

20242416250597

Biomedical engineering ; Elastomers ; Forecasting ; Magnetic fields ; Plastics ; Robotic arms ; Shear flow

Biomedical Engineering:461.1 ; Fluid Flow, General:631.1 ; Magnetism: Basic Concepts and Phenomena:701.2 ; Robotics:731.5 ; Polymer Products:817.1 ; Elastomers:818.2 ; Numerical Methods:921.6

ENGINEERING

2-s2.0-85195610876

Scopus

Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Li，Xin,Yu，Wenkai,Zhu，Xiaoyan,et al. Geometrically exact 3D arbitrarily curved rod theory for dynamic analysis: Application to predicting the motion of hard-magnetic soft robotic arm[J]. Applied Mathematical Modelling,2024,134:71-96.

Li，Xin,Yu，Wenkai,Zhu，Xiaoyan,Liu，Ju,&Yuan，Hongyan.(2024).Geometrically exact 3D arbitrarily curved rod theory for dynamic analysis: Application to predicting the motion of hard-magnetic soft robotic arm.Applied Mathematical Modelling,134,71-96.

Li，Xin,et al."Geometrically exact 3D arbitrarily curved rod theory for dynamic analysis: Application to predicting the motion of hard-magnetic soft robotic arm".Applied Mathematical Modelling 134(2024):71-96.