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Please use this identifier to cite or link to this item: http://hdl.handle.net/11299/58443

Title: The Foppl-von Karman equations for plates with incompatible strains
Authors: Lewicka, Marta
Mahadevan, L.
Pakzad, Reza
Keywords: non-Euclidean plates
nonlinear elasticity
Gamma convergence
calculus of variations
Issue Date: 24-Feb-2010
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.
URI: http://purl.umn.edu/58443
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