Hyperelasticity and the potentialness of a nonlinear operator
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A quasilinear second order partial differential operator of divergence form, involving N unknown functions and independent variables is transformed into a nonlinear functional operator in a Hilbert space. The constraint of potenlialness imposed on the nonlinear operator is seen to be equivalent in the case N=3 to hyperelasticity in the differential operator of elasiticity. By imposing further conditions on the differential operator, and assuming it is polynomial in the Frechet derivative of the unknown functions it becomes possible to extend to finite hyperelasticity a result proved earlier for infinitesimal hyperelasticity.
KeywordsHilbert Space Differential Operator Unknown Function Divergence Form Functional Operator
- N. Bourbaki,Elements of Mathematics - General Topology part I, (English Translation) Addison-Wesley Pubblishing Company, 1966.Google Scholar
- M. M. Vainberg,Variational Methods for the study of Non-linear Operators, Holden-Day, Inc., 1964.Google Scholar
- I. Hlaváček andJ. Necăs,On Inequalities of Korn’s type I, Arch. Rat. Mech. Anal.36, 4, (1970), pp. 305–311.Google Scholar
- C. Truesdell andW. Noll,The Non-linear field theories of Mechanics, Encyclopedia of Physics vol. III‖3, Springer-Verlag, Berlin, Heidelberg, New York, 1965.Google Scholar