Browsing by Author "Mahadevan, L."

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    The Foppl-von Karman equations for plates with incompatible strains
    (2010-02-24) Lewicka, Marta; Mahadevan, L.; Pakzad, Reza
    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.