Vol. 12, No. 5, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 5, 563–722
Issue 4, 353–561
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Subscriptions
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Author Index
To Appear
 
ISSN: 1559-3959
Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality

Sebastian Bahamonde, Christian G. Böhmer and Patrizio Neff

Vol. 12 (2017), No. 5, 689–710
Abstract

Modeling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become nonchiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically nonlinear Cosserat-type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our nonlinear approach. Plane wave solutions are briefly discussed within this model.

Keywords
Cosserat continuum, geometrically nonlinear micropolar elasticity, chiral materials, planar models
Mathematical Subject Classification 2000
Primary: 74J35, 74A35, 74J30, 74A30
Milestones
Received: 13 May 2017
Revised: 9 August 2017
Accepted: 14 August 2017
Published: 22 November 2017
Authors
Sebastian Bahamonde
Department of Mathematics
University College London
London
United Kingdom
Christian G. Böhmer
Department of Mathematics
University College London
London
United Kingdom
Patrizio Neff
Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik
Universität Duisburg-Essen
Essen
Germany