Variational theory for spatial rods

Steigmann, David J.; Faulkner, M.G.

doi:10.1007/bf00042633

Cited by 82 publications

(78 citation statements)

References 26 publications

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“…[28][29][30][31][32][33][34][35] in order to design new and enriched metamaterials. It is also very interesting the extension to the 3D case using the suggestions reported in [36].…”

Section: Discussionmentioning

confidence: 90%

Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

Turco

Dell’Isola

Rizzi

et al. 2016

Mechanics Research Communications

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“…[28][29][30][31][32][33][34][35] in order to design new and enriched metamaterials. It is also very interesting the extension to the 3D case using the suggestions reported in [36].…”

Section: Discussionmentioning

confidence: 90%

Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

Turco

Dell’Isola

Rizzi

et al. 2016

Mechanics Research Communications

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“…This is a constrained minimization problem, and we need to extend the classical variational derivation [9,7,13,26,6,2] of the equations of equilibrium for thin rods to take into account the presence of the kinematical constraints C d and C g , and of an internal variable η(S).…”

Section: Principle Of Virtual Work For a Ribbonmentioning

confidence: 99%

“Wunderlich, Meet Kirchhoff”: A General and Unified Description of Elastic Ribbons and Thin Rods

Dias¹,

Audoly²

2016

The Mechanics of Ribbons and Möbius Bands

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The equations for the equilibrium of a thin elastic ribbon are derived by adapting the classical theory of thin elastic rods. Previously established ribbon models are extended to handle geodesic curvature, natural out-ofplane curvature, and a variable width. Both the case of a finite width (Wunderlich's model) and the limit of small width (Sadowksky's model) are recovered. The ribbon is assumed to remain developable as it deforms, and the direction of the generatrices is used as an internal variable. Internal constraints expressing inextensibility are identified. The equilibrium of the ribbon is found to be governed by an equation of equilibrium for the internal variable involving its second-gradient, by the classical Kirchhoff equations for thin rods, and by specific, thin-rod-like constitutive laws; this extends the results of Starostin and van der Heijden (2007) to a general ribbon model. Our equations are applicable in particular to ribbons having geodesic curvature, such as an annulus cut out in a piece of paper. Other examples of application are discussed. By making use of a material frame rather than the Frenet-Serret frame, the present work unifies the description of thin ribbons and thin rods.

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“…Coleman et al reviewed dynamical equations in the theories of Kirchhoff and Clebsch (24). Steigmann and Faulkner derived the equations of classical rod theory using parameter-dependent variational approach (25). Recently, Gonzalez and Maddocks devised a method to extract sequence-dependent parameters for a rigid basepair DNA model from molecular dynamics simulation (26).…”

Section: Literature Reviewmentioning

confidence: 99%

Conformational analysis of stiff chiral polymers with end-constraints

Kim

Chirikjian

2006

Molecular Simulation

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We present a Lie-group-theoretic method for the kinematic and dynamic analysis of chiral semiflexible polymers with end constraints. The first is to determine the minimum energy conformations of semi-flexible polymers with end constraints, and the second is to perform normal mode analysis based on the determined minimum energy conformations. In this paper, we use concepts from the theory of Lie groups and principles of variational calculus to model such polymers as inextensible or extensible chiral elastic rods with coupling between twisting and bending stiffnesses, and/or between twisting and extension stiffnesses. This method is general enough to include any stiffness and chirality parameters in the context of elastic filament models with the quadratic elastic potential energy function. As an application of this formulation, the analysis of DNA conformations is discussed. We demonstrate our method with examples of DNA conformations in which topological properties such as writhe, twist, and linking number are calculated from the results of the proposed method. Given these minimum energy conformations, we describe how to perform the normal mode analysis. The results presented here build both on recent experimental work in which DNA mechanical properties have been measured, and theoretical work in which the mechanics of nonchiral elastic rods has been studied.

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Variational theory for spatial rods

Cited by 82 publications

References 26 publications

Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

“Wunderlich, Meet Kirchhoff”: A General and Unified Description of Elastic Ribbons and Thin Rods

Conformational analysis of stiff chiral polymers with end-constraints

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