Polyconvexity and Existence Theorem for Nonlinearly Elastic Shells

Abstract

We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic materials, that is to elastic materials possessing a stored energy function. Under some specific conditions of polyconvexity, coerciveness and growth of the stored energy function, we prove the existence of global minimizers. In addition, we define a general class of polyconvex stored energy functions which satisfies a coerciveness inequality.

13 pages

References in corpus (1)

• Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations

Cited by in corpus (3)

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