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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 (2016) A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation Calculus of Variations and Partial Differential Equations.

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Abstract

In this note we formulate a sufficient condition for the quasiconvexity at $x \mapsto \l x$ 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 M\"{u}ller and Spector, on admissible deformations. Deformations obey the condition $u(x)= \lambda x$ 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 $\lambda_0>0$ such that for every $\lambda\in (0,\lambda_0]$ it holds that $I(u) \geq I(u_{\lambda})$ for all admissible $u$, where $u_{\lambda}$ is the linear map $x \mapsto \lambda x$ applied across the entire domain. This is the quasiconvexity condition referred to above.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Bevan, JJUNSPECIFIEDUNSPECIFIED
Zeppieri, CIUNSPECIFIEDUNSPECIFIED
Date : 1 September 2016
Identification Number : 10.1007/s00526-016-0973-z
Related URLs :
Additional Information : The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-016-0973-z
Depositing User : Symplectic Elements
Date Deposited : 16 Mar 2016 09:58
Last Modified : 16 Mar 2016 09:58
URI: http://epubs.surrey.ac.uk/id/eprint/810239

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