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Reduced theories in nonlinear elasticity
Lewicka, Marta (2010)

Reduced theories in nonlinear elasticity


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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.

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Preprints [18]

ML was partially supported by the NSF grants DMS-0707275 and DMS-0846996

Suggested Citation
Lewicka, Marta. (2010). Reduced theories in nonlinear elasticity. Retrieved from the University of Minnesota Digital Conservancy,

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