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Rotational elasticity and couplings to linear elasticity

Boehmer, CG; Tamanini, N; (2010) Rotational elasticity and couplings to linear elasticity. Mathematics and Mechanics of Solids 10.1177/1081286513511093. Green open access

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Abstract

It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of static linear elasticity. An appropriate kinetic energy is identified and we present a dynamical model of rotational elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity. Moreover, parameter ranges are identified where the model describes an auxetic material. However, in all cases the potential energy functional is positive definite. Finally, we couple the rotational waves to linear elastic waves to study the behaviour of the coupled system. We find wave like solutions to the coupled equations and can visualise our results with the help of suitable figures.

Type: Article
Title: Rotational elasticity and couplings to linear elasticity
Open access status: An open access version is available from UCL Discovery
DOI: 10.1177/1081286513511093
Publisher version: http://dx.doi.org/10.1177/1081286513511093
Language: English
Additional information: This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 3.0 License (http://www.creativecommons.org/licenses/by-nc/3.0/) which permits non-commercial 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(http://www.uk.sagepub.com/aboutus/openaccess.htm).
Keywords: math-ph, math-ph, cond-mat.mtrl-sci, math.AP, math.MP
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/121573
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