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.

UR - http://www.scopus.com/inward/record.url?scp=84905115508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905115508&partnerID=8YFLogxK

U2 - 10.1007/s00205-014-0754-9

DO - 10.1007/s00205-014-0754-9

M3 - Article

AN - SCOPUS:84905115508

VL - 214

SP - 143

EP - 182

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 1

ER -