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|Title: ||Reduced theories in nonlinear elasticity|
|Authors: ||Lewicka, Marta|
|Keywords: ||non-Euclidean plates|
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.|
|Permanent URL: ||http://purl.umn.edu/90858|
|Appears in Collections:||Preprints|
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