NIST logo

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

NIST Authors in Bold

Author(s): B Yang; Vinod K. Tewary;
Title: Continuum Dyson's Equation and Defect Green's Function in a Heterogeneous Anisotropic Solid
Published: July 01, 2004
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
Pages: pp. 405 - 414
Keywords: anisotropic elasticity;continuum Dyson's equation;eigenstrain;Green's function;heterogeneity;inhomogeneous inclusion
Research Areas: Materials Science
PDF version: PDF Document Click here to retrieve PDF version of paper (370KB)