A weak approach to finite elasticity |
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Authors: | M Giaquinta G Modica J Souček |
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Institution: | (1) Dipartimento di Matematica Applicata, Università di Firenze, Via S. Marta 3, I-50139 Firenze, Italy;(2) Matematický Ústav, Akademie v d eské republiky, itná, 25, 11567 Praha, R |
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Abstract: | On the ground of four axioms we define thekinematics of perfectly elastic bodies and in particular the notion ofweak deformations of a perfectly elastic body. Weak deformations turn out to agree withweak diffeomorphisms introduced in 10], a class of rectifiable currents which enjoys good closure and compactness properties. Defining thedynamics of perfectly elastic bodies in terms of twoconstitutive conditions on the stored energy function, we can therefore prove existence of stable equilibrium weak deformations for mixed boundary value problems, which moreover satisfy equilibrium and conservation equations.This work has been partially supported by the Ministero dell'Universitá e della Ricerca Scientifica, by C.N.R. contract n. 91.01343.CT01, by the European Research Project GADGET, and by Grant n.11957 of the zech Acad. of Sciences.This article was processed by the author using the LaTEX style filepljour1 from Springer-Verlag. |
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Keywords: | 49Q20 73C50 |
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