Continuum Dyson's Equation and Defect Green's Function in a Heterogeneous Anisotropic Solid

Published

July 1, 2004

Author(s)

B Yang, Vinod Tewary

Abstract

Continuum Dyson's equation and defect Green's function (GF) in a heterogeneous, anisotropic and linearly elastic solid under homogeneous boundary conditions have been introduced. The continuum Dyson's equation relates the point-force Green's responses of two systems of identical geometry and boundary conditions but of different media. Given the GF of either system (i.e., a reference), the GF of the other (i.e., a defect system with defectivechange of materials property relative to the reference) can be obtained by solving the Dyson's equation. The defect GF is applied to solve the eigenstrain problem of a heterogeneous solid. In particular, the problem of slightly inhomogeneous inclusions is examined in detail. Based on the Dyson's equation, approximate schemes are proposed to efficiently evaluate the elastic field. Numerical results are reported for inhomogeneous inclusions in a semi-infinite substrate with a traction-free surface to demonstrate the validity of the present formulation.

Citation

Mechanics Research Communications

Volume

31

Issue

no. 4

Pub Type

Journals

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Keywords

anisotropic elasticity, continuum Dyson's equation, eigenstrain, Green's function, heterogeneity, inhomogeneous inclusion

Citation

Yang, B. and Tewary, V. (2004), Continuum Dyson's Equation and Defect Green's Function in a Heterogeneous Anisotropic Solid, Mechanics Research Communications, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=851371 (Accessed May 20, 2026)

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