TY - JOUR
T1 - A Polyconvex Integrand; Euler-Lagrange Equations and Uniqueness of Equilibrium
AU - Awi, Roméo
AU - Gangbo, Wilfrid
PY - 2014/10
Y1 - 2014/10
N2 - In this manuscript we are interested in stored energy functionals W defined on the set of d × d matrices, which not only fail to be convex but satisfy (Formula presemted.). We initiate a study which we hope will lead to a theory for the existence and uniqueness of minimizers of functionals of the form (Formula presented.), as well as their Euler-Lagrange equations. The techniques developed here can be applied to a class of functionals larger than those considered in this manuscript, although we keep our focus on polyconvex stored energy functionals of the form (Formula presented.) - such that (Formula presented.) - which appear in the study of Ogden material. We present a collection of perturbed and relaxed problems for which we prove uniqueness results. Then, we characterize these minimizers by their Euler-Lagrange equations.
AB - In this manuscript we are interested in stored energy functionals W defined on the set of d × d matrices, which not only fail to be convex but satisfy (Formula presemted.). We initiate a study which we hope will lead to a theory for the existence and uniqueness of minimizers of functionals of the form (Formula presented.), as well as their Euler-Lagrange equations. The techniques developed here can be applied to a class of functionals larger than those considered in this manuscript, although we keep our focus on polyconvex stored energy functionals of the form (Formula presented.) - such that (Formula presented.) - which appear in the study of Ogden material. We present a collection of perturbed and relaxed problems for which we prove uniqueness results. Then, we characterize these minimizers by their Euler-Lagrange equations.
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U2 - 10.1007/s00205-014-0754-9
DO - 10.1007/s00205-014-0754-9
M3 - Article
AN - SCOPUS:84905115508
SN - 0003-9527
VL - 214
SP - 143
EP - 182
JO - Archive For Rational Mechanics And Analysis
JF - Archive For Rational Mechanics And Analysis
IS - 1
ER -