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Plate theory for stressed heterogeneous multilayers of finite bending energy
We derive plate theory for (possibly slightly stressed) heterogeneous multilayers in the regime of finite bending energies from three-dimensional elasticity theory by means of $\Gamma$-convergence. This extends results in [G. Friesecke, R. D. James, S. Müller, Comm. Pure Appl. Math. 55 (2002), 1461-1506] and [B. Schmidt, MPI MIS preprint 111/2005] to non-homogeneous materials. As expected from the homogeneous case, we obtain a limiting energy functional depending on the second fundamental form of the plate surface. The effective elastic constants of the heterogeneous films will turn out to depend on the moments of the pointwise elastic constants of the materials.