Title:

On the geometric structure of the stress and strain tensors, dual variables and objective rates in continuum mechanics

Creator:

Sansour, C.

Publisher:

Polish Scientific Publishers IFTR

Place of publishing:

Warszawa

Date issued/created:

1992

Description:

Od Vol. 43, issue 1 (1991) wyd.: Polish Scientific Publishers = PWN ; Od Vol. 50, issue 4 (1998) wyd.: Agencja Reklamowo-Wydawnicza A. Grzegorczyk ; Od Vol. 53, issue 4/5 (2001) wyd: PAS. IFTR ; [1], 489-698 s. ; 24 cm

Type of object:

Journal/Article

Subject and Keywords:

Mechanika stosowana - czasopisma [KABA]

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.

Relation:

Archives of Mechanics

Volume:

44

Issue:

5-6

Start page:

527

End page:

556

Resource type:

Text

Detailed Resource Type:

Journal

Format:

application/pdf

Source:

IPPT PAN, call no. P.262 ; click here to follow the link

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Institute of Fundamental Technological Research of the Polish Academy of Sciences

Original in:

Library of the Institute of Fundamental Technological Research of The Polish Academy of Sciences

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open