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Plate theory for stressed heterogeneous multilayers of finite bending energy. (English) Zbl 1116.74034
Summary: We derive a 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 and S. Müller, Commun. Pure Appl. Math. 55, No. 11, 1461–1506 (2002; Zbl 1021.74024); B. Schmidt, Calc. Var. Partial Differ. Equ. 30, No. 4, 477–497 (2007; Zbl 1129.49045)] 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 turn out to depend on the moments of the pointwise elastic constants of the materials.

MSC:
74K20 Plates
74E05 Inhomogeneity in solid mechanics
74Q15 Effective constitutive equations in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
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