On the Convexity of Nonlinear Elastic Energies in the Right Cauchy-Green Tensor |
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Authors: | David Yang Gao Patrizio Neff Ionel Roventa Christian Thiel |
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Institution: | 1.School of Applied Science,Federation University Australia,Mt Helen,Australia;2.Fakult?t für Mathematik,Universit?t Duisburg-Essen,Essen,Germany;3.Department of Mathematics,University of Craiova,Craiova,Romania |
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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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