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Journal of Elasticity

, Volume 135, Issue 1–2, pp 457–483 | Cite as

Hyper-stresses in \(k\)-Jet Field Theories

  • Reuven SegevEmail author
  • Jędrzej Śniatycki
Article
  • 19 Downloads

Abstract

For high-order continuum mechanics and classical field theories configurations are modeled as sections of general fiber bundles and generalized velocities are modeled as variations thereof. Smooth stress fields are considered and it is shown that three distinct mathematical stress objects play the roles of the traditional stress tensor of continuum mechanics in Euclidean spaces. These objects are referred to as the variational hyper-stress, the traction hyper-stress and the non-holonomic stress. The properties of these three stress objects and the relations between them are studied.

Keywords

Continuum mechanics Classical field theories Fiber bundle Hyper-stress High order continuum mechanics 

Mathematics Subject Classification

74A10 70S10 53Z05 58A32 

Notes

Acknowledgements

Both authors are grateful to BIRS for sponsoring the Banff Workshop on Material Evolution, June 11–18, 2017, which led to this collaboration. R.S.’s work has been partially supported by H. Greenhill Chair for Theoretical and Applied Mechanics and the Pearlstone Center for Aeronautical Engineering Studies at Ben-Gurion University.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Departments of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  3. 3.University of VictoriaVictoriaCanada

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