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The Foppl-von Karman equations for plates with incompatible strains
Lewicka, Marta; Mahadevan, L.; Pakzad, Reza (2010)
 

Title 
The Foppl-von Karman equations for plates with incompatible strains

Issue Date
2010-02-24

Type
Preprint

Abstract
We provide a derivation of the Foppl-von Karman equations for the shape of and stresses in an elastic plate with residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three dimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive other low-dimensional descriptions of active materials.

Appears in Collection(s)
Preprints [18]

Suggested Citation
Lewicka, Marta; Mahadevan, L.; Pakzad, Reza. (2010). The Foppl-von Karman equations for plates with incompatible strains. Retrieved from the University of Minnesota Digital Conservancy, http://purl.umn.edu/58443.


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