Vol. 6, No. 2, 2018

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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

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 k-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.

high-order continuum mechanics, differential geometry, vector bundle, hyper-stress, traction, multilinear algebra
Mathematical Subject Classification 2010
Primary: 74A10
Secondary: 53Z05
Received: 28 October 2017
Revised: 8 February 2018
Accepted: 21 March 2018
Published: 29 May 2018

Communicated by Francesco dell'Isola
Reuven Segev
Department of Mechanical Engineering
Ben-Gurion University of the Negev
Jędrzej Śniatycki
Department of Mathematics and Statistics
University of Victoria
Victoria, BC
Department of Mathematics and Statistics
University of Calgary
Calgary, AL