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.
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Anicic, S. Polyconvexity and Existence Theorem for Nonlinearly Elastic Shells. J Elast 132, 161–173 (2018). https://doi.org/10.1007/s10659-017-9664-z
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DOI: https://doi.org/10.1007/s10659-017-9664-z
Keywords
- Shell
- Existence
- Minimizer
- Polyconvexity
- Hyperelasticity
- Nonlinear elasticity
- Helfrich energy
- Calculus of variations