Open Access

ARTICLE

Green's Function for Multilayers with Interfacial Membrane and Flexural Rigidities¹

by B. Yang², V. K. Tewary³

1 Contribution of the National Institute of Standards and Technology, an agency of the US government; not subject to copyright.
2 Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 32901
3 Materials Reliability Division, National Institute of Standards and Technology, Boulder, CO 80305

Computers, Materials & Continua 2008, 8(1), 23-32. https://doi.org/10.3970/cmc.2008.008.023

Abstract

A three-dimensional Green's function for a material system consisting of anisotropic and linearly elastic planar multilayers with interfacial membrane and flexural rigidities has been derived. The Stroh formalism and two-dimensional Fourier transforms are applied to derive the general solution for each homogeneous layer. The Green's function for the multilayers is then solved by imposing the surface boundary condition, the interfacial displacement continuity condition, and the interfacial traction discontinuity condition. The last condition is given by the membrane and bending equilibrium equations of the interphases modeled as Kirchhoff plates. Numerical results that demonstrate the validity and efficiency of the formulation are presented for the case of a stack of silicon thin films embedded in epoxy.

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Keywords

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