Mesoscale simulation of grain growth

David Kinderlehrer, Jeehyun Lee, Irene Livshits, Anthony Rollett, Shlomo Ta'asan

Research output: Contribution to journalConference articlepeer-review

16 Citations (Scopus)


Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.

Original languageEnglish
Pages (from-to)1057-1062
Number of pages6
JournalMaterials Science Forum
Issue numberII
Publication statusPublished - 2004
EventProceedings of the Second Joint International Conferences on Recrystallization and Grain Growth, ReX and GG2, SF2M - Annecy, France
Duration: 2004 Aug 302004 Sept 3

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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