On the Convexity of Nonlinear Elastic Energies in the Right Cauchy-Green Tensor
Yang Gao, D. and Neff, P. and Roventa, I. and Thiel, C.
JOURNAL OF ELASTICITY
Volume: 127 Pages: 303-308
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) = Wˆ (FTF) = Wˆ (C) which are convex with respect to the right Cauchy-Green tensor C= FTF, where F denotes the gradient of deformation. Examples of such energies exhibiting a blow up for det F→ 0 are given. © 2016, Springer Science+Business Media Dordrecht.