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Please use this identifier to cite or link to this item: http://hdl.handle.net/11299/90858

Title: Reduced theories in nonlinear elasticity
Authors: Lewicka, Marta
Keywords: non-Euclidean plates
nonlinear elasticity
calculus of variations
Issue Date: 9-Jun-2010
Abstract: The purpose of this note is to report on the recent development concerning the analysis and the rigorous derivation of thin film models for structures with nontrivial geometry. This includes: (i) shells with mid-surface of arbitrary curvature, and (ii) plates exhibiting residual stress at free equilibria. In the former setting, we derive a full range of models, some of them previously absent from the physics and engineering literature. The latter phenomenon has been observed in different contexts: growing leaves, torn plastic sheets and specifically engineered polymer gels. After reviewing available results, we list open problems with a promising angle of approach.
URI: http://purl.umn.edu/90858
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