@misc{Sansour_C._On_1992,
 author={Sansour, C.},
 volume={44},
 number={5-6},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Archives of Mechanics},
 howpublished={online},
 year={1992},
 publisher={Polish Scientific Publishers IFTR},
 language={eng},
 abstract={The geometric structure of the stress and strain tensors arising in continuum mechanics is investigated. All tensors are classified into two families, each consists of two subgroups regarded as physically equivalent since they are isometric. Special attention is focussed on the Cauchy stress tensor and it is proved that, corresponding to it, no dual strain measure exists. Some new stress tensors are formulated and the physical meaning of the stress tensor dual to the Almansi strain tensor is made apparent by employing a new decomposition of the Cauchy stress tensor with respect to a Lagrangian basis. It is shown that push- forward/pull-back under the deformation gradient applied to two work conjugate stress and strain tensors do not result in further dual tensors. The rotation field is incorporated as an independent variable by considering simple materials as constrained Cosserat continua. By the geometric structure of the involved tensors, it is claimed that only the Lie derivative with respect to the flow generated by the rotation group (Green-Naghdi objective rate) can be considered as occurring naturally in solid mechanics and preserving the physical equivalence in rate form.},
 type={Text},
 title={On the geometric structure of the stress and strain tensors, dual variables and objective rates in continuum mechanics},
 URL={http://www.rcin.org.pl/Content/68378/PDF/WA727_18037_44-5-6-1992_AMS_Sansour-05.pdf},
 keywords={Mechanika stosowana - czasopisma [KABA]},
}