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Contact problems of hyperelastic membranes: existence theory
Author(s) -
Andrä H.,
Warby M. K.,
Whiteman J. R.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(20000710)23:10<865::aid-mma140>3.0.co;2-t
Subject(s) - hyperelastic material , mathematics , variational inequality , isotropy , ogden , compressibility , mathematical analysis , convexity , calculus (dental) , mechanics , physics , finite element method , thermodynamics , medicine , dentistry , quantum mechanics , financial economics , economics
In this paper we describe the pressure‐driven inflation of an incompressible isotropic hyperelastic mem brane into a rigid mould by a variational inequality and consider the existence of a solution in the case of various, suitably modified, strain energy functions of the Ogden form. The variational inequality description is applicable to the case of perfect sliding contact of the membrane with the mould and the modification to the strain energy function is according to tension field theory which rules out compressive stresses. The modified or relaxed strain energy functions obtained are shown, in our examples, to be polyconvex and in some cases convex. Using such properties, the main result of the paper is an existence theorem for a solution of the variational inequality. Copyright © 2000 John Wiley & Sons, Ltd.