The problem of a thin film coated on an elastic layer and subject to a thermal variation is analytically investigated in the present work. The analysis is developed in order to assess the mechanical behaviour of a crystalline undulator designed for obtaining high emission radiations through channelling phenomenon.It consists in a plane silicon wafer alternately patterned with thin films in silicon nitride on both surfaces. The system adopts a periodic curvature as a result of the misfit strain due to the different thermal expansivities of the layer and the film. The problem is governed by an integral equation which can be reduced to a linear algebraic system by approximating the unknown interfacial shear stress via series expansion of Chebyshev polynomials.

Thermally induced deformations in a partially coated elastic layer / Lanzoni, L.; Radi, Enrico. - In: INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES. - ISSN 0020-7683. - ELETTRONICO. - 46 (6)(2009), pp. 1402-1412.

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