On the Bending and Twisting of Rods with Misfit

Robert V. Kohn; Ethan O’Brien

doi:10.1007/s10659-017-9635-4

On the Bending and Twisting of Rods with Misfit

Robert V. Kohn, Ethan O’Brien

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive a one-dimensional variational problem representing the elastic energy of a rod with misfit, starting from a nonlinear, three-dimensional elastic energy with nontrivial preferred strain. Our approach to dimension reduction is to find a Gamma-limit as the thickness of the rod tends to 0. The limiting energy is a quadratic function of the rates at which the rod bends and twists, and we give explicit expressions for the preferred curvature and twist in the special case of isotropic elastic moduli.

Original language	English (US)
Pages (from-to)	115-143
Number of pages	29
Journal	Journal of Elasticity
Volume	130
Issue number	1
DOIs	https://doi.org/10.1007/s10659-017-9635-4
State	Published - Jan 1 2018

Keywords

Dimension reduction
Elastic rods
Gamma-convergence
Misfit

ASJC Scopus subject areas

General Materials Science
Mechanics of Materials
Mechanical Engineering

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10.1007/s10659-017-9635-4

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abstract = "We derive a one-dimensional variational problem representing the elastic energy of a rod with misfit, starting from a nonlinear, three-dimensional elastic energy with nontrivial preferred strain. Our approach to dimension reduction is to find a Gamma-limit as the thickness of the rod tends to 0. The limiting energy is a quadratic function of the rates at which the rod bends and twists, and we give explicit expressions for the preferred curvature and twist in the special case of isotropic elastic moduli.",

keywords = "Dimension reduction, Elastic rods, Gamma-convergence, Misfit",

author = "Kohn, {Robert V.} and Ethan O{\textquoteright}Brien",

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N2 - We derive a one-dimensional variational problem representing the elastic energy of a rod with misfit, starting from a nonlinear, three-dimensional elastic energy with nontrivial preferred strain. Our approach to dimension reduction is to find a Gamma-limit as the thickness of the rod tends to 0. The limiting energy is a quadratic function of the rates at which the rod bends and twists, and we give explicit expressions for the preferred curvature and twist in the special case of isotropic elastic moduli.

AB - We derive a one-dimensional variational problem representing the elastic energy of a rod with misfit, starting from a nonlinear, three-dimensional elastic energy with nontrivial preferred strain. Our approach to dimension reduction is to find a Gamma-limit as the thickness of the rod tends to 0. The limiting energy is a quadratic function of the rates at which the rod bends and twists, and we give explicit expressions for the preferred curvature and twist in the special case of isotropic elastic moduli.

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On the Bending and Twisting of Rods with Misfit

Abstract

Keywords

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