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A Variational Principle and Numerical Scheme for Microstructural Evolution of Materials Controlled By Lattice Diffusion

In: Computational Mechanics

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  • Jingzhe Pan

    (University of Leicester, Department of Engineering)

Abstract

This paper re-examines the variational principle for microstructure evolution controlled by lattice diffusion and proposes a numerical scheme for computer simulation of the evolution. Nabarro-Herring creep of engineering alloys and sintering of ceramic powders are two typical examples of such evolution. We consider the case where only the grain-boundary and free surface act as the source and sink of matter. A linear kinetic law for the lattice diffusion is assumed. The boundary integration technique is used to satisfy the governing equations inside each individual grain. This means that all the degrees of freedom are defined on the network of grain-boundary and free surface except for those describing the rigid motion of each grain. When simulating large scale microstructural evolution, frequent remeshing of the microstructure has to be performed. The proposed numerical scheme offers a distinctive advantage because only the interface network needs to be remeshed. The variational principle is part of a unified variational principle for solid state diffusion and the numerical scheme can be readily integrated into the scheme previously developed so that microstructural evolution controlled by solid state diffusion along free surface and grain-boundary as well as through the grain lattice can be numerically simulated.

Suggested Citation

  • Jingzhe Pan, 2007. "A Variational Principle and Numerical Scheme for Microstructural Evolution of Materials Controlled By Lattice Diffusion," Springer Books, in: Computational Mechanics, pages 80-87, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75999-7_7
    DOI: 10.1007/978-3-540-75999-7_7
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