Engineering Mechanics

International Conference

Proceedings Vol. 12 (2006)


May 15 – 18, 2006, Svratka, Czech Republic
Editors: Jiří Náprstek and Cyril Fischer

Copyright © 2006 Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, Prague

ISBN 80-86246-27-2 (printed, Extended Abstracts)
ISSN 1805-8248 (printed)
ISSN 1805-8256 (electronic)

list of papers scientific commitee

Stress rate and incremental principle of virtual work in finite deformations
Z. Fiala
pages 56 - +12p., full text

Solution of finite deformation problems is sought in the space of all deformation tensor fields. Representation of a deformation process here as a trajectory makes us possible to further classify symmetric second-order tensor fields either as points, vectors, or covectors, and, as a consequence, assign them the corresponding time derivatives. However, as the space of all deformation tensor fields has proved non-euclidean, the time derivative of vector, and covector fields along the trajectory should be defined by the covariant derivative. This approach enables us coherently to formulate an incremental principle of virtual work, and propose the corresponding procedure in solving finite deformation problems. The approach will be demonstrated in finite elasticity. T. Frankel: ”Physics and engineering readers would profit greatly if they would form the habit of translating the vectorial and tensorial statements found in their customary reading of physical articles and books into the language of differential geometry, and of using its methods.” [Frankel 1997, p.xxiii] L. Schwartz: ”Engineers and physicists should take note that virtual work is simply the natural duality between cotangent and tangent bundles.” [BAMS 2003, p.411]

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