Zusammenfassung
We derive a two-dimensional model for elastic plates as a Gamma-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl ...
Zusammenfassung
We derive a two-dimensional model for elastic plates as a Gamma-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl Math 55: 1461-1506, 2002). We extend their result to the case of p growth at infinity with p is an element of [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries in W(2,2) isometries, which was obtained by Pakzad (J Differ Geom 66:47-69, 2004) for convex domains and by Hornung (Comptes Rendus Mathematique 346:189-192, 2008) for piecewise C(1) domains.
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