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On jets, almost
symmetric tensors, and traction hyper-stresses
Reuven Segev and Jędrzej Śniatycki
Vol. 6 (2018), No. 2, 101–124
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Abstract |
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This paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational -th order hyper-stress is an object that acts on jets of generalized velocities to produce power densities. The traction hyper-stress is introduced as an object that induces hyper-traction fields on the boundaries of subbodies. Additional aspects of multilinear algebra relevant to the analysis of these objects are reviewed. |
Keywords
high-order continuum mechanics, differential geometry,
vector bundle, hyper-stress, traction, multilinear algebra
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Mathematical Subject Classification 2010
Primary: 74A10
Secondary: 53Z05
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Milestones
Received: 28 October 2017
Revised: 8 February 2018
Accepted: 21 March 2018
Published: 29 May 2018
Communicated by Francesco dell'Isola
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Authors |
| Reuven Segev | |
| Department of Mechanical
Engineering Ben-Gurion University of the Negev Beer-Sheva Israel |
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| Jędrzej Śniatycki | |
| Department of Mathematics and
Statistics University of Victoria Victoria, BC Canada |
Department of Mathematics and
Statistics University of Calgary Calgary, AL Canada |
