Experiments on snap buckling, hysteresis and loop formation in twisted rods

Goss, V.G.A.; Heijden, G. H. M. van der; Thompson, J. M. T.; Neukirch, Sébastien

doi:10.1007/bf02428182

Cited by 71 publications

(60 citation statements)

References 19 publications

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“…Van der Heijden et al [5,6] describe the writhing of cylindric metallic wires as multiaxial experiments for clamped rods. The experimental procedure is shown in Fig.…”

Section: Multiaxial Experimentsmentioning

confidence: 99%

“…Similar to van der Heijden et al [5,6], simulations of these experiments based on our implementation of a Cosserat rod have been performed for the material parameters of nitinol. The results are shown in Fig.…”

Section: Simulationmentioning

confidence: 99%

“…Section 2.5.2 deals with the design of suitable multiaxial experiments for the characterization of cables and hoses. In a first approach, we test straight clamped cables and hoses in large deformation experiments combining bending, torsion and tension after van der Heijden et al [5,6]. Since these experiments will prove to be not useful for characterizing cables and hoses, new simplified multiaxial experiments for clamped cables are designed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards Viscoplastic Constitutive Models for Cosserat Rods

Dörlich¹,

Linn²,

Scheffer³

et al. 2016

Archive of Mechanical Engineering

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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 viscoplastic constitutive law formulated in the terms of sectional quantities of Cosserat rods. Since the loading of cables in applications is in most cases not represented by these mostly uniaxial classical experiments, but rather multiaxial, new experiments for cables have to be designed. They have to illustrate viscoplastic effects, enable access to (viscoplastic) material parameters and account for coupling effects between different deformation modes. This work focuses on the design of such experiments.

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“…Van der Heijden et al [5,6] describe the writhing of cylindric metallic wires as multiaxial experiments for clamped rods. The experimental procedure is shown in Fig.…”

Section: Multiaxial Experimentsmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards Viscoplastic Constitutive Models for Cosserat Rods

Dörlich¹,

Linn²,

Scheffer³

et al. 2016

Archive of Mechanical Engineering

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show abstract

“…This subsequently grows into a lateral ply as the experiment progresses under slowly decreasing Z (figure 3f ). More comprehensive experiments are reported by Goss et al (2005).…”

Section: Laboratory Experiments On Ply Formationmentioning

confidence: 99%

Single-molecule magnetic tweezer tests on DNA: bounds on topoisomerase relaxation

Thompson

2008

Proc. R. Soc. A.

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Biomedical researchers regularly stretch and twist single DNA molecules in magnetic tweezer experiments. By making the molecule writhe into a plectoneme (ply) and plotting its load-extension curves, key DNA parameters, such as effective radius, can be estimated. Adding untangling enzymes (topoisomerases) to the DNA's environment, their individual cuts are detected as jumps in extension.Sufficient information is now known about the topoisomerases for us to make good idealizations about their kinematics and mechanics. The novelty of this paper is to study their actions in the context of accurate ply solutions from the theory of elastic rods. To do this, we define an extended rod-plus-tension system that allows us to determine the stored energies from areas in the conventional link versus writhe plane.After a cut, the molecule relaxes dynamically to a new equilibrium state, and often there will be two or more alternative stable configurations onto which it might settle. Knowing the energy levels allows us to identify which states can and cannot be reached over the unstable mountain passes, and which of the accessible states offer the greatest energy relaxation. Strict energy bounds on behaviour are established.This knowledge has medical value because topoisomerase inhibitors, lethal for cells, are used as antibiotics and in chemotherapy for cancer.

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“…Critical points on td plots are useful to know when considering the stability of solutions, especially for many physical rigid loading problems where it is the axial component of the force t that is measured at the clamped end for a given input d; see, for example, [16]. From Eq.…”

Section: Horizontal Force-displacement (Td) Plotmentioning

confidence: 99%

Critical points of the clamped–pinned elastica

Singh

Goss

2018

Acta Mech

Self Cite

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We investigate equilibrium configurations of the clamped-pinned elastica where the pinned end can be displaced towards, and past, the clamped end. Solving the nonlinear ordinary differential equation for the clamped-pinned elastica for any mode in terms of elliptic integrals, we find sets of equations which govern the equilibrium configurations for given displacements. Equilibrium configurations for various displacements of the pinned end and any mode are obtained by numerically solving those sets of equations. A physical quantity, such as the force that arises in the elastica due to displacement of the pinned end, is taken to be a function of displacement. Although it is generally not possible to define a physical quantity as a function of displacement explicitly, an equation for the rate of change of this physical quantity with respect to displacement can be found by partial differentiation of the sets of equations which govern the equilibrium configurations. Setting that rate of change to zero provides a constraint equation for locating the critical points of that physical quantity. That constraint equation and the sets of equations which govern the equilibrium configurations are solved numerically to obtain the critical points of the physical quantity. Our procedure is demonstrated by finding local extrema on force-displacement plots (useful when analysing the stability of equilibrium configurations) and the maximum deflection of the elastica. Finally, we suggest how our procedure has scope for wider application.

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Experiments on snap buckling, hysteresis and loop formation in twisted rods

Cited by 71 publications

References 19 publications

Towards Viscoplastic Constitutive Models for Cosserat Rods

Towards Viscoplastic Constitutive Models for Cosserat Rods

Single-molecule magnetic tweezer tests on DNA: bounds on topoisomerase relaxation

Critical points of the clamped–pinned elastica

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