One-forms on spaces of embeddings: a frame work for constitutive laws in elasticity
Abstract
The present contribution to this volume is concerned with certain problems in non-linear functional analysis which are motivated by classical physics, specifically by elasticity theory:we are given a «body»,i.e. a compact smooth manifold
which moves and may be deformed in some
(equipped with a fixed inner product); we assume that the motion and deformation are such that the diffeomorphism type of
does not change. Hence,
is the image under a smooth embedding of some compact smooth manifold M (possibly with boundary
) and the appropriate configuration space for the problem is the set
of smooth embeddings
; this set is a smooth Fréchet manifold when endowed with its natural
-topology.
![M'](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c0c8156de7a5455113e67f33c15182fb.png)
![R<sup>n</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8709922046aaf17601461c6edd5c0c49.png)
![M'](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c0c8156de7a5455113e67f33c15182fb.png)
![M'](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c0c8156de7a5455113e67f33c15182fb.png)
![\partial M](http://siba-ese.unile.it/plugins/generic/latexRender/cache/e89a2ceedc8d45f4439e85b04dea1d2e.png)
![E( M, R<sup>n</sup>)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4dcfbad1318055b3f650971f523b6f96.png)
![M→ R<sup>n</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/e9f03de421c6369cce1e801ea3342051.png)
![C^∈fty](http://siba-ese.unile.it/plugins/generic/latexRender/cache/f81ee5189c2bb2ede892f7ccf8f1eb69.png)
DOI Code:
10.1285/i15900932v11p21
Full Text: PDF