Polyconvexity and existence theorem for nonlinearly elastic shells. (English) Zbl 1393.74103
Summary: 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.
MSC:
| 74K25 | Shells |
| 74B20 | Nonlinear elasticity |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
| 74G25 | Global existence of solutions for equilibrium problems in solid mechanics (MSC2010) |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
shell; existence; minimizer; polyconvexity; hyperelasticity; nonlinear elasticity; Helfrich energy; calculus of variationsReferences:
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