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Geometrically
nonlinear Cosserat elasticity in the plane: applications to
chirality
Sebastian Bahamonde, Christian G. Böhmer and Patrizio Neff |
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Vol. 12 (2017), No. 5, 689–710
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 74J35, 74A35, 74J30, 74A30
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Milestones
Received: 13 May 2017
Revised: 9 August 2017
Accepted: 14 August 2017
Published: 22 November 2017
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Authors |
| Sebastian Bahamonde | |
| Department of Mathematics University College London London United Kingdom |
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| Christian G. Böhmer | |
| Department of Mathematics University College London London United Kingdom |
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| Patrizio Neff | |
| Lehrstuhl für Nichtlineare Analysis
und Modellierung, Fakultät für Mathematik Universität Duisburg-Essen Essen Germany |
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