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Friesecke, Gero; James, Richard D.; Müller, Stefan

A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. (English) Zbl 1100.74039

Arch. Ration. Mech. Anal. 180, No. 2, 183-236 (2006).
The authors use the \(\Gamma\)-convergence method for deriving of a hierarchy of plate models from three-dimensional nonlinear elasticity formulation. In this way, they analyze the membrane theory, von Kármán theory and certain theories of constraints. Different limit models are obtained using different scalings of elastic energy per unit volume and of the strenght of applied force with respect to the thickness of the plate. In the conclusion, the authors summarize the obtained results and, in the case of von Kármán theory, explain how the criticism of Truesdell and Antman can be addressed by means of authors’ method. Finally, important open problems are formulated which cannot be approached by means of the \(\Gamma\)-convergence.
Reviewer: Oldřich John (Praha)

Cited in 6 Reviews
Cited in 228 Documents

MSC:

74K20 Plates
74B20 Nonlinear elasticity
74Q05 Homogenization in equilibrium problems of solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure

Keywords:

membrane theory; von Kármán theory
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References:

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