2010/02/11 by Marta Lewicka, L. Mahadevan, Reza Pakzad · 1 citation
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.MP #msc:74K20 #msc:74B20
paper · pdf · doi:10.1098/rspa.2010.0138
26 pages
arxiv created 2010/02/11 · arxiv updated 2015/05/18
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.