Euler-Lagrange Equations for Nonlinearly Elastic Rods with Self-Contact

Schuricht, Friedemann; Mosel, Heiko von der

doi:10.1007/s00205-003-0253-x

Cited by 51 publications

(49 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will call this a generalized Poisson criterion, and it will allow us to calculate absolute volumes in our analysis. Previously, in studies of helical topologies a criterion preventing the tube from bending into itself has been considered [2,3,14]. These two criteria are mathematically identical though their motivations can be phrased differently.…”

Section: Generalized Poisson Criterionmentioning

confidence: 99%

The generic geometry of helices and their close-packed structures

Olsen

Bohr

2009

Theor Chem Acc

View full text Add to dashboard Cite

The formation of helices is an ubiquitous phenomenon for molecular structures whether they are biological, organic, or inorganic, in nature. Helical structures have geometrical constraints analogous to closepacking of three-dimensional crystal structures. For helical packing the geometrical constraints involve parameters such as the radius of the helical cylinder, the helical pitch angle, and the helical tube radius. In this communication, the geometrical constraints for single helix, double helix, and for double helices with minor and major grooves are calculated. The results are compared with values from the literature for helical polypeptide backbone structures, the a-, p-, 3 10 -, and c-helices. The a-helices are close to being optimally packed in the sense of efficient use of space, i.e. close-packed. They are also more densely packed than the other three types of helices. For double helices comparisons are made to the A, B, and Z forms of DNA. The helical geometry of the A form is nearly close-packed. The packing density for the B and Z forms of DNA are found to be approximately equal to each other.

show abstract

Section: Generalized Poisson Criterionmentioning

confidence: 99%

The generic geometry of helices and their close-packed structures

Olsen

Bohr

2009

Theor Chem Acc

View full text Add to dashboard Cite

show abstract

“…The constraint on the radius of the centerline is then given by a prescribed positive lower bound on the global radius of curvature function as one varies among all possible triplets of distinct points along the curve (compare Lemma 2). Their formulation is an analytically tractable notion of 'hard contact' and has inspired a sequence of papers addressing various existence and regularity questions of this formulation [7,31,36]. Coleman and Swigon [10,9] developed tests on the second-order variation to determine which equilibria correspond to minima for elastic rod models where opposing forces are introduced at points of self-contact, whereas van der Heijden et al [37] focus on finding bifurcation diagrams that identify and classify "jump phenomena" at points of self-contact.…”

Section: Introductionmentioning

confidence: 99%

A Variational Rod Model with a Singular Nonlocal Potential

Hoffman

Seidman

2010

Arch Rational Mech Anal

View full text Add to dashboard Cite

In the classic theory of elastic rods, two non-adjacent points along the rod may upon contact occupy the same physical space. We develop an elastic rod model with a pairwise repulsive potential such that if two non-adjacent points along the rod are close in physical space, there is an energy barrier that prevents contact. For adjacent pairs, the repulsive potential is negligible and the elastic rod is described by a classical elastic rod model. The framework for this model is developed to prove the existence of minimizers within each homotopy class, where the idea of topological homotopy of a curve is generalized to a framed curve, or an elastic rod. Finally, the first-order necessary conditions are derived.

show abstract

“…This is carried out for the (nonlinearly) elastic contact with a rigid obstacle in Schuricht [16], [17] and for the elastic self-contact of rods in Schuricht & v.d. Mosel [18]. In the present paper we extend these investigations to the contact of two elastic bodies.…”

Section: Introductionmentioning

confidence: 83%