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Journal articles on the topic 'Cosserat rod-theory'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Zhang, Hou Bin, Mao Sheng Jiang, and Ying Wu. "A Cosserat Rod Model of Multi-Symplectic Structure and its Numerical Treatment." Advanced Materials Research 712-715 (June 2013): 1395–400. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.1395.

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In this paper, a Hamiltonian formulation of the Cosserat rod model is proposed. The model, based on the Cossert rod theory incorporates shear, elongation, flexure and twist deformation, is of multi-symplectic structure. A multi-symplectic algorithm is employed to discretize the equation and a numerical example is giving.

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2

Beliaev, Mikhail, Vladimir Lalin, and Vladimir Kuroedov. "Geometrically Nonlinear Rods Theory - Comparison of the Results Obtained by Cosserat-Timoshenko and Kirchhoff's Rod Theories." Applied Mechanics and Materials 725-726 (January 2015): 629–35. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.629.

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Up to the present solutions for geometrically nonlinear rods were obtained only by the Kirchhoff’s theory. This theory disregards flexibility of the rod on tension and shear. For rods in modern software suites the Cosserat-Timoshenko rod theory is generally used. As opposed to Kirchhoff’s theory it takes into account tensile and shear stiffness. This paper presents solutions obtained by Cosserat-Timoshenko rod theory. These results can be used as benchmark problem for verification of software suites.

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3

Rubin, M. B. "Free Vibration of a Rectangular Parallelepiped Using the Theory of a Cosserat Point." Journal of Applied Mechanics 53, no. 1 (1986): 45–50. http://dx.doi.org/10.1115/1.3171736.

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Free vibration of a rectangular parallelepiped composed of a homogeneous linear elastic isotropic material is studied. The parallelepiped is modeled as an isotropic Cosserat point and simple formulas are developed to predict the lowest frequencies of vibration. Within the context of the theory, extensional and shear vibrations are uncoupled. The lowest extensional frequency predicted by the Cosserat theory is compared with available exact solutions and with predictions of thin rod theory. Finally, by introducing a simple modification of the director inertia coefficient it is shown that the Cos

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Rubin, M. B. "Equivalence of a Constrained Cosserat Theory and Antman’s Special Cosserat Theory of a Rod." Journal of Elasticity 140, no. 1 (2020): 39–47. http://dx.doi.org/10.1007/s10659-019-09761-9.

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5

Wang, Honghong, Jingli Du, and Yi Mao. "Cosserat Rod-Based Tendon Friction Modeling, Simulation, and Experiments for Tendon-Driven Continuum Robots." Micromachines 16, no. 3 (2025): 346. https://doi.org/10.3390/mi16030346.

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Traditional tendon-driven continuum robot (TDCR) models based on Cosserat rod theory often assume that tendon tension is a continuous wrench along the backbone. However, this assumption overlooks critical factors, including the discrete arrangement of disks, the segmented configuration of tensioned tendons, and the friction between tendons and guide holes. Additionally, tendon forces are not continuous but discrete, concentrated wrenches, with the frictional force magnitude and direction varying based on the TDCR’s bending configuration. We propose a TDCR modeling method that integrates Cosser

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6

Rubin, M. B. "Numerical Solution Procedures for Nonlinear Elastic Curved Rods Using the Theory of a Cosserat Point." Mathematics and Mechanics of Solids 10, no. 1 (2005): 89–126. http://dx.doi.org/10.1177/1081286504033005.

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The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the theory of a Cosserat point. Although the general theory is valid for curved rods, the constitutive coefficients have been determined by comparison with exact linear solutions only for straight beams. The objective of this paper is to explore the accuracy of the predictions of the Cosserat theory for curved rods by comparison with exact solutions. Specifically, these problems include: linearized axisymmetric deformation of a circular ring loaded with internal and external p

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Alqumsan, Ahmad Abu, Suiyang Khoo, and Michael Norton. "Robust control of continuum robots using Cosserat rod theory." Mechanism and Machine Theory 131 (January 2019): 48–61. http://dx.doi.org/10.1016/j.mechmachtheory.2018.09.011.

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8

Bhashi, Bhashi, S. Sreejath, and S. P. Singh. "Experimentation Evaluation of Dynamics of Steel Wire Rope." Key Engineering Materials 996 (December 6, 2024): 133–42. https://doi.org/10.4028/p-wtr6ta.

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Wire ropes represent a distinct category of ropes synthesized through the intertwining or braiding of individual steel wires. This unique construction confers notable attributes such as strength, flexibility, and durability to the resultant rope. The pervasive wire ropes across diverse industries underscores their capacity to adeptly manage substantial loads and endure adverse environmental conditions finding its application in mechanical, civil, mining, and marine engineering. This paper presents usage of image processing method to detect the deflection of a steel wire rope. The system compri

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9

Smriti, Ajeet Kumar, Alexander Großmann, and Paul Steinmann. "A thermoelastoplastic theory for special Cosserat rods." Mathematics and Mechanics of Solids 24, no. 3 (2018): 686–700. http://dx.doi.org/10.1177/1081286517754132.

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A general framework is presented to model coupled thermoelastoplastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable, together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well-known nonlinear theory of thermoelasticity for special Cosserat rods. Later on, additive decomposition is used to separate the ther

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10

Linn, J., H. Lang, and A. Tuganov. "Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping." Mechanical Sciences 4, no. 1 (2013): 79–96. http://dx.doi.org/10.5194/ms-4-79-2013.

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Abstract. We present the derivation of a simple viscous damping model of Kelvin–Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, strain rates that vary slowly compared to internal relaxation processes, and a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of b

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11

Lalin, Vladimir Vladimirovich, and Daria Aleksandrovna Kushova. "New Results in Dynamics Stability Problems of Elastic Rods." Applied Mechanics and Materials 617 (August 2014): 181–86. http://dx.doi.org/10.4028/www.scientific.net/amm.617.181.

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This article is about the nonlinear dynamic stability problems of the exact (Cosserat) theory of elastic rods. There is examined the general geometrically nonlinear theory with no restrictions on displacements and rotations being imposed. In this article, it is shown that the variational problem can be defined as the search for the stationary point of the Hamilton’s functional. The new exact solutions of the stability problems for different types of the end fixities of the rod were obtained taking into account bending, shear and longitudinal stiffness.

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12

Till, John, Vincent Aloi, and Caleb Rucker. "Real-time dynamics of soft and continuum robots based on Cosserat rod models." International Journal of Robotics Research 38, no. 6 (2019): 723–46. http://dx.doi.org/10.1177/0278364919842269.

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The dynamic equations of many continuum and soft robot designs can be succinctly formulated as a set of partial differential equations (PDEs) based on classical Cosserat rod theory, which includes bending, torsion, shear, and extension. In this work we present a numerical approach for forward dynamics simulation of Cosserat-based robot models in real time. The approach implicitly discretizes the time derivatives in the PDEs and then solves the resulting ordinary differential equation (ODE) boundary value problem (BVP) in arc length at each timestep. We show that this strategy can encompass a w

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Lalin, Vladimir, and Daria Kushova. "Correct Formulation of the Stability Problem for Timoshenko Beam." Applied Mechanics and Materials 725-726 (January 2015): 854–62. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.854.

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This article is about the nonlinear problems of the theory of elastic Cosserat – Timoshenko’s rods in the material (Lagrangian) description with energy conjugated vectors of forces, moments and strains. The variational formulations of static problems was given. The differential equations of the plane stability problems were obtained from the second variation of the Lagrangian functional. The exact solutions of the stability problems for basic types of the end fixities of the rod were obtained for the Timoshenko’s rod (taking into account only bending and shear stiffness). It appears that class

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14

Miśkiewicz, Mikołaj. "Structural response of existing spatial truss roof construction based on Cosserat rod theory." Continuum Mechanics and Thermodynamics 31, no. 1 (2018): 79–99. http://dx.doi.org/10.1007/s00161-018-0660-8.

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15

Jung, Pascal, Sigrid Leyendecker, Joachim Linn, and Michael Ortiz. "A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria." International Journal for Numerical Methods in Engineering 85, no. 1 (2010): 31–60. http://dx.doi.org/10.1002/nme.2950.

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16

Dörlich, Vanessa, Joachim Linn, Tobias Scheffer, and Stefan Diebels. "Towards Viscoplastic Constitutive Models for Cosserat Rods." Archive of Mechanical Engineering 63, no. 2 (2016): 215–30. http://dx.doi.org/10.1515/meceng-2016-0012.

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Abstract Flexible, slender structures like cables, hoses or wires can be described by the geometrically exact Cosserat rod theory. Due to their complex multilayer structure, consisting of various materials, viscoplastic behavior has to be expected for cables under load. Classical experiments like uniaxial tension, torsion or three-point bending already show that the behavior of e.g. electric cables is viscoplastic. A suitable constitutive law for the observed load case is crucial for a realistic simulation of the deformation of a component. Consequently, this contribution aims at a viscoplasti

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17

ARNE, WALTER, NICOLE MARHEINEKE, and RAIMUND WEGENER. "ASYMPTOTIC TRANSITION FROM COSSERAT ROD TO STRING MODELS FOR CURVED VISCOUS INERTIAL JETS." Mathematical Models and Methods in Applied Sciences 21, no. 10 (2011): 1987–2018. http://dx.doi.org/10.1142/s0218202511005635.

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This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory, we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, R

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18

ARNE, WALTER, NICOLE MARHEINEKE, ANDREAS MEISTER, and RAIMUND WEGENER. "NUMERICAL ANALYSIS OF COSSERAT ROD AND STRING MODELS FOR VISCOUS JETS IN ROTATIONAL SPINNING PROCESSES." Mathematical Models and Methods in Applied Sciences 20, no. 10 (2010): 1941–65. http://dx.doi.org/10.1142/s0218202510004738.

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This work deals with the curling behavior of slender viscous jets in rotational spinning processes. In terms of slender-body theory, an instationary incompressible viscous Cosserat rod model is formulated which differs from the approach of Ribe et al.,18 in the incompressibility approximation and reduces to the string model of Marheineke and Wegener13 for a vanishing slenderness parameter. Focusing exclusively on viscous and rotational effects on the jet in the exit plane near the spinning nozzle, the stationary two-dimensional scenario is described by a two-point boundary value problem of a s

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19

Pratt, Richard L., Brooke E. Suesser, and Andrew J. Petruska. "Observed Control of Magnetic Continuum Devices." Robotics 12, no. 1 (2023): 11. http://dx.doi.org/10.3390/robotics12010011.

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This paper models an extensible catheter with an embedded magnet at its distal tip subject to an external magnetic field. We implement a control method coined observed control to perform model-based predictive control of the catheter using a Kalman smoother framework. Using this same smoother framework, we also solve for catheter shape and orientation given magnetic and insertion control using Cosserat rod theory and implement a disturbance observer for closed-loop control. We demonstrate observed control experimentally by traversing a 3D cube trajectory with the catheter tip. The catheter ach

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20

Ghafoori, Morteza, and Ali Keymasi Khalaji. "Modeling and experimental analysis of a multi-rod parallel continuum robot using the Cosserat theory." Robotics and Autonomous Systems 134 (December 2020): 103650. http://dx.doi.org/10.1016/j.robot.2020.103650.

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21

Shelukhin, Vladimir. "Flows of Linear Polymer Solutions and Other Suspensions of Rod-like Particles: Anisotropic Micropolar-Fluid Theory Approach." Polymers 13, no. 21 (2021): 3679. http://dx.doi.org/10.3390/polym13213679.

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We formulate equations governing flows of suspensions of rod-like particles. Such suspensions include linear polymer solutions, FD-virus, and worm-like micelles. To take into account the particles that form and their rotation, we treat the suspension as a Cosserat continuum and apply the theory of micropolar fluids. Anisotropy of suspensions is determined through the inclusion of the microinertia tensor in the rheological constitutive equations. We check that the model is consistent with the basic principles of thermodynamics. In addition to anisotropy, the theory also captures gradient bandin

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22

Roshanfar, Majid, Javad Dargahi, and Amir Hooshiar. "Cosserat Rod-Based Dynamic Modeling of a Hybrid-Actuated Soft Robot for Robot-Assisted Cardiac Ablation." Actuators 13, no. 1 (2023): 8. http://dx.doi.org/10.3390/act13010008.

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Soft robotics has emerged as a promising field due to the unique characteristics offered by compliant and flexible structures. Overcoming the challenge of precise position control is crucial in the development of such systems that require accurate modeling of soft robots. In response, a hybrid-actuated soft robot employing both air pressure and tendons was proposed, modeled, and validated using the dynamic Cosserat rod theory. This approach comprehensively addresses various aspects of deformation, including bending, torsion, shear, and extension. The designed robot was intended for robot-assis

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Edelmann, Janis, Andrew J. Petruska, and Bradley J. Nelson. "Magnetic control of continuum devices." International Journal of Robotics Research 36, no. 1 (2017): 68–85. http://dx.doi.org/10.1177/0278364916683443.

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In this paper we apply Cosserat rod theory to catheters with permanent magnetic components that are subject to spatially varying magnetic fields. The resulting model formulation captures the magnetically coupled catheter behavior and provides numerical solutions for rod equilibrium configurations in real-time. The model is general, covering cases with different catheter geometries, multiple magnetic components, and various boundary constraints. The necessary Jacobians for quasi-static, closed-loop control using an electromagnetic coil system and a motorized advancer are derived and incorporate

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24

Chen, Zhi, Aicheng Zou, Zhantian Qin, Xingguo Han, Tianming Li, and Shengkai Liu. "Modeling and Fabrication of Soft Actuators Based on Fiber-Reinforced Elastomeric Enclosures." Actuators 10, no. 6 (2021): 127. http://dx.doi.org/10.3390/act10060127.

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Unlike rigid actuators, soft actuators can easily adapt to complex environments. Understanding the relationship between the deformation of soft actuators and external factors such as pressure would enable rapid designs based on specific requirements, such as flexible, compliant endoscopes. An effective model is demonstrated that predicts the deformation of a soft actuator based on the virtual work principle and the geometrically exact Cosserat rod theory. The deformation process is analyzed for extension, bending, and twisting modules. A new manufacturing method is then introduced. Through any

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Shelukhin, Vladimir. "Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid." Mathematics 11, no. 23 (2023): 4740. http://dx.doi.org/10.3390/math11234740.

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To tackle suspensions of particles of any shape, the thermodynamics of a Cosserat continuum are developed by the method suggested by Landau and Khalatnikov for the mathematical description of the super-fluidity of liquid 2He. Such an approach allows us to take into account the rotation of particles and their form. The flows of suspensions of neutrally buoyant rod-like particles are considered in detail. These suspensions include linear polymer solutions, FD-virus and worm-like micelles. The anisotropy of the suspensions is determined through the inclusion of the micro-inertia tensor in the rhe

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26

Dehghani, Mohammad, and S. Ali A. Moosavian. "Dynamics Modeling of a Continuum Robotic Arm with a Contact Point in Planar Grasp." Journal of Robotics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/308283.

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Grasping objects by continuum arms or fingers is a new field of interest in robotics. Continuum manipulators have the advantages of high adaptation and compatibility with respect to the object shape. However, due to their extremely nonlinear behavior and infinite degrees of freedom, continuum arms cannot be easily modeled. In fact, dynamics modeling of continuum robotic manipulators is state-of-the-art. Using the exact modeling approaches, such as theory of Cosserat rod, the resulting models are either too much time-taking for computation or numerically unstable. Thus, such models are not suit

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Kuznetsova, Daria, Vladimir Lalin, and Nikolay Malkov. "THE EFFECT OF THE AXIAL AND SHEAR STIFFNESSES ON ELASTIC ROD’S STABILITY." International Journal for Computational Civil and Structural Engineering 18, no. 4 (2022): 62–70. http://dx.doi.org/10.22337/2587-9618-2022-18-4-62-70.

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This article is about the nonlinear problems of the theory of elastic Cosserat – Timoshenko’s rods in the material (Lagrangian) description. The variational definition for the problem as finding the stationary point of the Lagrangian functional and differential formulation of static problems were given. The exact stability functional and stability equations of the plane problem for physically linear elastic rods taking into account the axial, shear and bending stiffnesses were received. The exact value of the critical load was obtained taking into account the axial, shear and bending deformati

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Shingo, Prothick Kumar, Md Ijaj Ahmed, Rathujan Vijayanathan, Pranto Das, and Md Mazbabur Rahman Sakib. "Innovations and Challenges in Soft Robotic Dynamics: Advanced Modeling, Interaction, and Control Mechanisms." European Journal of Theoretical and Applied Sciences 2, no. 5 (2024): 760–73. http://dx.doi.org/10.59324/ejtas.2024.2(5).67.

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Soft robots are a rapidly growing field of robotics that uses compliant and deformable materials to create systems that can have differently shaped adaptive forces in unstructured environments. Because they are self-contained and inherently safe for human-robot interaction, these robots have potentially wide applications, including medical devices, industrial automation, machine inspection equipment, or environmental monitoring. Nevertheless, soft robots present unique challenges in design and control, especially when it comes to dynamic modeling and real-time control, given their infinite deg

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Prothick, Kumar Shingo, Ijaj Ahmed Md, Vijayanathan Rathujan, Das Pranto, and Mazbabur Rahman Sakib Md. "Innovations and Challenges in Soft Robotic Dynamics: Advanced Modeling, Interaction, and Control Mechanisms." European Journal of Theoretical and Applied Sciences 2, no. 5 (2024): 760–73. https://doi.org/10.59324/ejtas.2024.2(5).67.

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Soft robots are a rapidly growing field of robotics that uses compliant and deformable materials to create systems that can have differently shaped adaptive forces in unstructured environments. Because they are self-contained and inherently safe for human-robot interaction, these robots have potentially wide applications, including medical devices, industrial automation, machine inspection equipment, or environmental monitoring. Nevertheless, soft robots present unique challenges in design and control, especially when it comes to dynamic modeling and real-time control, given their infinite deg

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Dong, Jiaxiang, Quanquan Liu, Peng Li, Chunbao Wang, Xuezhi Zhao, and Xiping Hu. "Design, Modeling, and Experimental Validation of a Bio-Inspired Rigid–Flexible Continuum Robot Driven by Flexible Shaft Tension–Torsion Synergy." Biomimetics 10, no. 5 (2025): 301. https://doi.org/10.3390/biomimetics10050301.

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This paper presents a bio-inspired rigid–flexible continuum robot driven by flexible shaft tension–torsion synergy, tackling the trade-off between actuation complexity and flexibility in continuum robots. Inspired by the muscular arrangement of octopus arms, enabling versatile multi-degree-of-freedom (DoF) movements, the robot achieves 6-DoF motion and 1-DoF gripper opening and closing movement with only six flexible shafts, simplifying actuation while boosting dexterity. A comprehensive kinetostatic model, grounded in Cosserat rod theory, is developed; this model explicitly incorporates the c

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Campisano, Federico, Simone Caló, Andria A. Remirez, et al. "Closed-loop control of soft continuum manipulators under tip follower actuation." International Journal of Robotics Research 40, no. 6-7 (2021): 923–38. http://dx.doi.org/10.1177/0278364921997167.

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Continuum manipulators, inspired by nature, have drawn significant interest within the robotics community. They can facilitate motion within complex environments where traditional rigid robots may be ineffective, while maintaining a reasonable degree of precision. Soft continuum manipulators have emerged as a growing subfield of continuum robotics, with promise for applications requiring high compliance, including certain medical procedures. This has driven demand for new control schemes designed to precisely control these highly flexible manipulators, whose kinematics may be sensitive to exte

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Rubin, M. B. "Angular Momentum in a Special Nonlinear Elastic Rod." Journal of Elasticity, March 22, 2024. http://dx.doi.org/10.1007/s10659-024-10061-0.

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AbstractIn the constrained Cosserat theory of a rod with a rigid cross-section, the balance of angular momentum is satisfied by a restriction on the constitutive equations that requires a second order tensor to be symmetric. The kinematics of the rod are determined by satisfying the balances of linear and director momentum and kinematic constraints. In contrast, the Antman model for a special Cosserat theory of rods proposes constitutive equations directly for the force and mechanical moment applied to the rod and the kinematics are determined by the balances of linear and angular momentum. Th

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Sun, Yuchen, Anup Teejo Mathew, Imran Afgan, Federico Renda, and Cecilia Laschi. "Real-time dynamics of soft manipulators with cross-sectional inflation: application to the octopus muscular hydrostat." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 481, no. 2314 (2025). https://doi.org/10.1098/rspa.2024.0642.

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Inspired by the embodied intelligence of biological creatures like the octopus, a soft robotic arm uses its highly flexible structure to perform various tasks in a complex environment. While the classic Cosserat rod theory investigates the bending, twisting, shearing and stretching of the soft arm, it fails to capture the in-plane deformation that occurs during certain tasks, particularly those involving active lateral traction. This paper introduces an extended Cosserat rod theory addressing these limitations by incorporating an extra strain variable, reflecting the in-plane inflation ratio.

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Fahim Golestaneh, Amirreza, Venanzio Cichella, and Caterina Lamuta. "Physics-based modeling of Twisted and Coiled Artificial Muscles (TCAMs) for soft robotics using extended Cosserat theory of rods." Smart Materials and Structures, April 3, 2025. https://doi.org/10.1088/1361-665x/adc90a.

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Abstract The current work develops a physics-based model for Twisted and Coiled Artificial Muscles (TCAMs) using the extended Cosserat theory of rods. These artificial muscles are lightweight and low-cost, generating a high power-to-weight ratio. They produce tensile forces up to 12,600 times their own weight, closely mimicking the functionality of biological muscles. The contraction of these muscles is driven by the anisotropic volume expansion of their twisted fibers, induced by deformation of the fibers' cross-section. Unlike prior models, this study implements the extended Cosserat theory,

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Fang, Chao, Ajeet Kumar, and Subrata Mukherjee. "A Finite Element Analysis of Single-Walled Carbon Nanotube Deformation." Journal of Applied Mechanics 78, no. 3 (2011). http://dx.doi.org/10.1115/1.4003191.

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Chandraseker et al. (2009, “An Atomistic-Continuum Cosserat Rod Model of Carbon Nanotubes,” J. Mech. Phys. Solids, 57, pp. 932–958), in a 2009 JMPS paper, proposed an atomistic-continuum model, based on Cosserat rod theory, for deformation of a single-walled carbon nanotube (SWNT). This model allows extension and twist, as well as shear and bending (in two directions) of a SWNT. This present paper proposes a finite element method (FEM) implementation of the above mentioned Cosserat rod model for a SWNT, subjected, in general, to axial and transverse loads, as well as bending moments and torque

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36

"Electromagnetic effects in the theory of rods." Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 314, no. 1530 (1985): 311–52. http://dx.doi.org/10.1098/rsta.1985.0021.

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This paper is concerned with the nonlinear and linear thermomechanical theories of deformable rod-like bodies in which account is taken of electromagnetic effects. The development is made by a direct approach with the use of the one-dimensional formulation of a theory of directed media called a Cosserat curve . The first part of the paper deals with the formulation of appropriate nonlinear equations governing the motion of a rod in the presence of electromagnetic and thermal effects. In the second part of the paper, emphasis is placed on the linearized version of the theory, a general discussi

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Burzyński, Stanisław. "On FEM analysis of Cosserat-type stiffened shells: static and stability linear analysis." Continuum Mechanics and Thermodynamics, October 27, 2020. http://dx.doi.org/10.1007/s00161-020-00928-7.

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Abstract The present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod, respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam FE with 6 DoFs (including the drilling rotation for shells) in each node. Examples of static and stability linear analyses are included. Novel design formu

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Manoharan, Sakthiprasad Kuttankulangara, and Rajesh Kannan Megalingam. "Coconut tree modeling based on abiotic factors and modified cosserat rod theory." Plant Methods 21, no. 1 (2025). https://doi.org/10.1186/s13007-025-01379-4.

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Abstract The biomechanics of growing trees, particularly coconut trees, are intricate due to various abiotic factors such as sunlight, wind, gravitropism, and cultivation practices. Existing structural growth models fail to capture the unique characteristics of coconut trees, which lack branches and have large crown leaves. This research introduces a novel coconut tree modeling approach, integrating abiotic factors and modified Cosserat rod theory. Factors like sunlight availability, wind speed, cultivation practices, and gravitropism influence coconut tree growth rates. The model encompasses

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Sun, Jiefeng, and Jianguo Zhao. "Physics-Based Modeling of Twisted-and-Coiled Actuators Using Cosserat Rod Theory." IEEE Transactions on Robotics, 2021, 1–18. http://dx.doi.org/10.1109/tro.2021.3104238.

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Pourghasemi Hanza, Sadegh, and Hamed Ghafarirad. "Mechanics of fiber-reinforced soft manipulators based on inhomogeneous Cosserat rod theory." Mechanics of Advanced Materials and Structures, January 29, 2023, 1–13. http://dx.doi.org/10.1080/15376494.2023.2170498.

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Arbind, A., A. R. Srinivasa, and J. N. Reddy. "A Higher-Order Theory for Open and Closed Curved Rods and Tubes Using a Novel Curvilinear Cylindrical Coordinate System." Journal of Applied Mechanics 85, no. 9 (2018). http://dx.doi.org/10.1115/1.4040335.

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In this study, the governing equation of motion for a general arbitrary higher-order theory of rods and tubes is presented for a general material response. The impetus for the study, in contrast to the classical Cosserat rod theories, comes from the need to study bulging and other deformation of tubes (such as arterial walls). While Cosserat rods are useful for rods whose centerline motion is of primary focus, here we consider cases where the lateral boundaries also undergo significant deformation. To tackle these problems, a generalized curvilinear cylindrical coordinate (CCC) system is intro

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Tummers, Matthias, Frédéric Boyer, Vincent Lebastard, et al. "Continuum concentric push–pull robots: A Cosserat rod model." International Journal of Robotics Research, September 10, 2024. http://dx.doi.org/10.1177/02783649241263366.

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Various approaches and structures emerged recently to design continuum robots. One of the most promising designs regards a new concept of continuum concentric push–pull robots (CPPRs) that have the characteristic of combining several key advantages of tendon actuated, multi-backbone, and concentric tube ones (direct curvature actuation, small outer/inner diameter ratio, free lumen, etc.). Geometrically-exact models of such recently introduced robots are yet to be developed to gain leverage of their full potential. This article extends beyond usual definitions of Cosserat rod theory in order to

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Chadha, Mayank, and Michael D. Todd. "A Generalized Approach for Reconstructing the Three-Dimensional Shape of Slender Structures Including the Effects of Curvature, Shear, Torsion, and Elongation." Journal of Applied Mechanics 84, no. 4 (2017). http://dx.doi.org/10.1115/1.4035785.

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This paper extends the approach for determining the three-dimensional global displaced shape of slender structures from a limited set of scalar surface strain measurements. It is an exhaustive approach that captures the effect of curvature, shear, torsion, and elongation. The theory developed provides both a determination of the uniaxial strain (in a given direction) anywhere in the structure and the deformed shape, given a set of strain values. The approach utilizes Cosserat rod theory and exploits a localized linearization approach that helps to obtain a local basis function set for the disp

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Garg, Mohit, and Ajeet Kumar. "A slender body theory for the motion of special Cosserat filaments in Stokes flow." Mathematics and Mechanics of Solids, May 10, 2022, 108128652210833. http://dx.doi.org/10.1177/10812865221083323.

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The motion of filament-like structures in fluid media has been a topic of interest since long. In this regard, a well known slender body theory exists, wherein the fluid flow is assumed to be Stokesian while the filament is modeled as a Kirchhoff rod which can bend and twist but remains inextensible and unshearable. In this work, we relax the inextensibility and unshearability constraints on filaments, i.e., the filament is modeled as a special Cosserat rod. Starting with the boundary integral formulation of Stokes flow involving the filament’s surface velocity and fluid traction that acts on

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Parvaresh, Aida, and S. Ali A. Moosavian. "Dynamics and path tracking of continuum robotic arms using data-driven identification tools." Robotica, August 9, 2021, 1–27. http://dx.doi.org/10.1017/s026357472100093x.

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Abstract In this paper, forward/inverse dynamics of a continuum robotic arm is developed using a data-driven approach, which could tackle uncertainties and extreme nonlinearities to obtain reliable solutions. By establishing a direct mapping between the actuator and task spaces, the unnecessary mappings of actuator-to-configuration then configuration-to-task are eliminated, to reduce extra computational cost. The proposed approach is validated through simulation (based on Cosserat rod theory) and experimental tests on RoboArm. Next, path tracking in the presence/absence of obstacles as well as

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Manfredo, Davide, Vanessa Dörlich, Joachim Linn, and Martin Arnold. "Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators." Multibody System Dynamics, May 4, 2023. http://dx.doi.org/10.1007/s11044-023-09910-y.

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AbstractThis contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods for the simulation of cables composed of complex interior components. Motivated by the basic elements of Cosserat rod theory, we develop a specific approach to constitutive modelling adapted for this application. Afterwards, we describe the hysteretical behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure bending experiments, slender structures such as electric cables behave inelastically, and open

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Todd, Michael D., Christopher J. Stull, and Michael Dickerson. "A Local Material Basis Solution Approach to Reconstructing the Three-Dimensional Displacement of Rod-Like Structures From Strain Measurements." Journal of Applied Mechanics 80, no. 4 (2013). http://dx.doi.org/10.1115/1.4023023.

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This paper presents a new approach for determining three-dimensional global displacement (for arbitrarily sized deformation) of thin rod or tetherlike structures from a limited set of scalar strain measurements. The approach is rooted in Cosserat rod theory with a material-adapted reference frame and a localized linearization approach that facilitates an exact local basis function set for the displacement along with the material frame. The solution set is shown to be robust to potential singularities from vanishing bending and twisting angle derivatives and from vanishing measured strain. Vali

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Zhao, Tian, Fabio Schneider-Jung, Joachim Linn, and Ralf Müller. "Simulation and parameterization of nonlinear elastic behavior of cables." Multibody System Dynamics, July 22, 2024. http://dx.doi.org/10.1007/s11044-024-10008-2.

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AbstractThis work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based

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Wang, Peiyi, Xinhua Yang, Xiangyang Wang, and Sheng Guo. "General Kinetostatic Modeling and Deformation Analysis of a Two-Module Rod-Driven Continuum Robot with Friction Considered." Chinese Journal of Mechanical Engineering 36, no. 1 (2023). http://dx.doi.org/10.1186/s10033-023-00893-7.

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AbstractContinuum robots actuated by flexible rods have large potential applications, such as detection and operation tasks in confined environments, since the push and pull actuation of flexible rods withstand tension and compressive force, and increase the structure’s rigidity. In this paper, a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established. Then, the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load character

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Luo, Ji, Panwen Wang, Pei Jiang, et al. "Dynamics of a Three-Dimensional Soft Fiber-Reinforced Manipulator With External Loads Based on Cosserat Rod Theory." IEEE/ASME Transactions on Mechatronics, 2025, 1–12. https://doi.org/10.1109/tmech.2025.3574706.

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