One-forms on spaces of embeddings: a frame work for constitutive laws in elasticity


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 M' which moves and may be deformed in some R<sup>n</sup> (equipped with a fixed inner product); we assume that the motion and deformation are such that the diffeomorphism type of M' does not change. Hence, M' is the image under a smooth embedding of some compact smooth manifold M (possibly with boundary \partial M) and the appropriate configuration space for the problem is the set E( M, R<sup>n</sup>) of smooth embeddings M→ R<sup>n</sup>; this set is a smooth Fréchet manifold when endowed with its natural C^∈fty-topology.

DOI Code: 10.1285/i15900932v11p21

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