Boundary Integral Analysis for Functionally Graded Materials

L. J. Gray, T. Kaplan, and J. Richardson
Computer Science and Mathematics Division, ORNL

G. Paulino
University of Illinois

P. Martin and J. R. Berger
Colorado School of Mines

Functionally graded materials (FGM) are an important new area of materials research in which two materials with very different properties are connected by a region where the material properties vary smoothly with position. They have applications in many areas including: superheat resistance (furnace liners and space structures), biomedical (dental and bone implants), military (vehicle and body armor), and dielectric materials (wave guides and radar avoidance). We have successfully derived the Green's function for an FGM wherein the material properties vary exponentially through the connecting region. The Green's function has been obtained in closed form for the Laplace equation (heat conduction), and in a readily computable form for elasticity. With these Green's function, an FGM analysis can be formulated as simply as for homogeneous media in terms of boundary integral equations, and we believe that this is the first serious application of this method to non-homogeneous media. The ability to perform computational analyses is highly important for FGM research and development, as the manufacturing and experimental testing of these materials (in its infancy) is not at all simple. In particular, parameter design optimization and crack propagation are two areas of major importance for which experimental techniques are of limited utility. For these types of analyses, boundary integral formulations have significant advantages over finite element methods, and thus having the Green's function will be especially useful.

Publications:

L. J. Gray, T. Kaplan, J. D. Richardson, and G. H. Paulino, "Green's Function and Boundary Integral Analysis for Exponentially Graded Materials: Heat Conduction," ASME Journal of Applied Mechanics (in press).

P. Martin, J. D. Richardson, L. J. Gray, and J. R. Berger, "Green's Functions for an Exponentially Graded Elastic Material," Proceedings of the Royal Society (in press).

Y.-S. Chan, L. J. Gray, T. Kaplan, and G. H. Paulino, "Green's Function for a Two-Dimensional Exponentially Graded Elastic Medium," Proceedings of the Royal Society (submitted).

3/14/00