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MiS Preprint
86/2006

Plate theory for stressed heterogeneous multilayers of finite bending energy

Bernd Schmidt

Abstract

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.

Received:
Aug 23, 2006
Published:
Aug 23, 2006
MSC Codes:
74K20, 49J45

Related publications

inJournal
2007 Repository Open Access
Bernd Schmidt

Plate theory for stressed heterogeneous multilayers of finite bending energy

In: Journal de mathématiques pures et appliquées, 88 (2007) 1, pp. 107-122