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A Finite Element Method for Simulating Interface Motion

Published online by Cambridge University Press:  10 February 2011

H.H. Yu  and
Z. Suo
H.H. Yu
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton Materials Institute, Princeton University, Princeton, NJ 08544
Z. Suo
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton Materials Institute, Princeton University, Princeton, NJ 08544
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Abstract

This paper describes our recent progress in developing a finite element method for simulating interface motion. Attention is focused on two mass transport mechanisms: interface migration and surface diffusion. A classical theory states that, for interface migration, the local normal velocity of an interface is proportional to the free energy reduction associated with a unit volume of atoms detach from one side of the interface and attach to the other side. We express this theory into a weak statement, in which the normal velocity and any arbitrary virtual motion of the interface relate to the free energy change associated with the virtual motion. An example with two degrees of freedom shows how the weak statement works. For a general case, we divide the interface into many elements, and use the positions of the nodes as the generalized coordinates. The variations of the free energy associated with the variations of the nodal positions define the generalized forces. The weak statement connects the velocity components at all the nodes to the generalized forces. A symmetric, positive-definite matrix appears, which we call the viscosity matrix. A set of nonlinear ordinary differential equations evolve the nodal positions. We then treat combined surface diffusion and evaporation-condensation in a similar method with generalized coordinates including both nodal positions and mass fluxes. Three numerical examples are included. The first example shows the capability of the method in dealing with anisotropic surface energy. The second example is pore-grain boundary separation in the final stage of ceramic sintering. The third example relates to the process of mass reflow in VLSI fabrication.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 529: Symposia BB – Computational & Mathematical Models of Microstructural Evolution , 1998 , 113
Copyright
Copyright © Materials Research Society 1998

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References

1 Thompson, C.V. and Lloyd, J.R., MRS Bulletin, December 1993, p. 19 (1993).Google Scholar
2 Suo, Z., Advances in Applied Mechanics 33, p. 194 (1997)Google Scholar
3 Sun, B., Suo, Z. and Yang, W., Acta Mater. 45, p. 1907 (1997).Google Scholar
4 Sun, B. and Suo, Z., Acta Mater. 45, p. 4953 (1997).Google Scholar
5 Herring, C., in The Physics of Powder Metallurgy, edited by Kingston, W.E., pp. 143–179, McGraw-Hill, New York (1951).Google Scholar
6 Yu, H.H. and Suo, Z., unpublished work.Google Scholar
7 Shewmon, P.G., Trans. Met. Soc. AIME 230, p. 1134 (1964).Google Scholar
8 Hsueh, C.H. and Evans, A.G., Acta Metall. 31, p.189 (1983).Google Scholar
9 Arita, Y., Awaya, N., Ohno, K. and Sato, M., MRS Bulletin 19, p.66 (1994).Google Scholar
10 Gardner, D.S. and Fraser, D.B., Presentation in MRS conference, spring, 1995.Google Scholar
11 Huang, H., Gilmer, G.H. and Rubia, T. D. de la, An atomic simulator for thin film deposition in three dimensions, preprint (1997).Google Scholar
12 Sun, B., Ph.D. thesis, University of California at Santa Barbara, p. 39 (1996).Google Scholar