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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.
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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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