Abstract
We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic energy functional. This criterion is applicable to energies \(W(F)=\widehat{W}(F^{T}F)=\widehat{W}(C)\) which are convex with respect to the right Cauchy-Green tensor \(C=F^{T}F\), where \(F\) denotes the gradient of deformation. Examples of such energies exhibiting a blow up for \(\det F\to0\) are given.
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Acknowledgements
We are grateful to S.J. Spector for his help, especially for pointing out Remark 2.3.
The third author was supported by Grant PN-II-RU-TE-2014-4-1109 of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI.
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Yang Gao, D., Neff, P., Roventa, I. et al. On the Convexity of Nonlinear Elastic Energies in the Right Cauchy-Green Tensor. J Elast 127, 303–308 (2017). https://doi.org/10.1007/s10659-016-9601-6
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DOI: https://doi.org/10.1007/s10659-016-9601-6