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arXiv · 1002.2252

The von Karman equations for plates with residual strain

Marta Lewicka·L. Mahadevan·Reza Pakzad
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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.

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Marta Lewicka, L. Mahadevan, Reza Pakzad. 2010-02-11. The von Karman equations for plates with residual strain. https://doi.org/10.1098/rspa.2010.0138

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