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A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation

Bevan, JJ and Zeppieri, CI (2015) A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation arXiv, 1507.0.

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Abstract

In this note we formulate a sufficient condition for the quasiconvexity at x -->Lx, where L>0, of certain functionals I(u) which model the stored-energy of elastic materials subject to a deformation u. The materials we consider may cavitate, and so we impose the well-known technical condition (INV), due to Muller and Spector, on admissible deformations. Deformations obey the condition u(x)= Lx whenever x belongs to the boundary of the domain initially occupied by the material. In terms of the parameters of the models, our analysis provides an explicit upper bound on those L>0 such that I(u) > I(u_L) for all admissible u, where u_L is the linear map x--> Lx applied across the entire domain. This is the quasiconvexity condition referred to above.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Bevan, JJUNSPECIFIEDUNSPECIFIED
Zeppieri, CIUNSPECIFIEDUNSPECIFIED
Date : 10 July 2015
Additional Information : This is an arXiv publication.
Depositing User : Symplectic Elements
Date Deposited : 14 Oct 2015 09:32
Last Modified : 14 Oct 2015 09:33
URI: http://epubs.surrey.ac.uk/id/eprint/808816

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