Proceedings Vol. 12 (2006)
ENGINEERING MECHANICS 2006
May 15 – 18, 2006, Svratka, Czech Republic
Copyright © 2006 Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, Prague
ISSN 1805-8248 (printed)
ISSN 1805-8256 (electronic)
list of papers scientific commitee
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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