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:

Czasopismo/Artykuł

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:

Tekst

Detailed Resource Type:

Czasopismo

Format:

application/pdf

Source:

IPPT PAN, sygn. P.262 ; click here to follow the link

Language:

eng

Language of abstract:

eng

Rights:

Licencja Creative Commons Uznanie autorstwa 4.0

Terms of use:

Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -

Digitizing institution:

Instytut Podstawowych Problemów Techniki Polskiej Akademii Nauk

Original in:

Biblioteka Instytutu Podstawowych Problemów Techniki PAN

Projects co-financed by:

Program Operacyjny Polska Cyfrowa, lata 2014-2020, Działanie 2.3 : Cyfrowa dostępność i użyteczność sektora publicznego; środki z Europejskiego Funduszu Rozwoju Regionalnego oraz współfinansowania krajowego z budżetu państwa

Access:

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