Plate theory for stressed heterogeneous multilayers of finite bending energy
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Submission date: 23. Aug. 2006
published in: Journal de mathématiques pures et appliquées, 88 (2007) 1, p. 107-122
DOI number (of the published article): 10.1016/j.matpur.2007.04.011
MSC-Numbers: 74K20, 49J45
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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 -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.