Böhmer, CG;
Lee, Y;
(2020)
Compatibility conditions of continua using Riemann–Cartan geometry.
Mathematics and Mechanics of Solids
10.1177/1081286520961453.
(In press).
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Abstract
The compatibility conditions for generalised continua are studied in the framework of differential geometry, in particular Riemann–Cartan geometry. We show that Vallée’s compatibility condition in linear elasticity theory is equivalent to the vanishing of the three-dimensional Einstein tensor. Moreover, we show that the compatibility condition satisfied by Nye’s tensor also arises from the three-dimensional Einstein tensor, which appears to play a pivotal role in continuum mechanics not mentioned before. We discuss further compatibility conditions that can be obtained using our geometrical approach and apply it to the microcontinuum theories.
| Type: | Article |
|---|---|
| Title: | Compatibility conditions of continua using Riemann–Cartan geometry |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1177/1081286520961453 |
| Publisher version: | https://doi.org/10.1177/1081286520961453 |
| Language: | English |
| Additional information: | https://creativecommons.org/licenses/by/4.0/This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access page |
| Keywords: | Compatibility conditions, Cosserat continuum, Riemann–Cartan geometry |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10109559 |
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