dorsal/arxiv
View SchemaAdvances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics
| Authors | Hashem M. Mourad, Krishna Garikipati |
|---|---|
| Categories | |
| ArXiv ID | physics/0411012 |
| URL | https://arxiv.org/abs/physics/0411012 |
| DOI | 10.1016/j.cma.2006.06.005 |
| Journal | Comput. Methods Appl. Mech. Engrg., vol. 196, no. 1--3, pp. 595--607, 2006. |
Abstract
This work is based upon a coupled, lattice-based continuum formulation that was previously applied to problems involving strong coupling between mechanics and mass transport; e.g. diffusional creep and electromigration. Here we discuss an enhancement of this formulation to account for migrating grain boundaries. The level set method is used to model grain-boundary migration in an Eulerian framework where a grain boundary is represented as the zero level set of an evolving higher-dimensional function. This approach can easily be generalized to model other problems involving migrating interfaces; e.g. void evolution and free-surface morphology evolution. The level-set equation is recast in a remarkably simple form which obviates the need for spatial stabilization techniques. This simplified level-set formulation makes use of velocity extension and field re-initialization techniques. In addition, a least-squares smoothing technique is used to compute the local curvature of a grain boundary directly from the level-set field without resorting to higher-order interpolation. A notable feature is that the coupling between mass transport, mechanics and grain-boundary migration is fully accounted for. The complexities associated with this coupling are highlighted and the operator-split algorithm used to solve the coupled equations is described.
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"abstract": "This work is based upon a coupled, lattice-based continuum formulation that\nwas previously applied to problems involving strong coupling between mechanics\nand mass transport; e.g. diffusional creep and electromigration. Here we\ndiscuss an enhancement of this formulation to account for migrating grain\nboundaries. The level set method is used to model grain-boundary migration in\nan Eulerian framework where a grain boundary is represented as the zero level\nset of an evolving higher-dimensional function. This approach can easily be\ngeneralized to model other problems involving migrating interfaces; e.g. void\nevolution and free-surface morphology evolution. The level-set equation is\nrecast in a remarkably simple form which obviates the need for spatial\nstabilization techniques. This simplified level-set formulation makes use of\nvelocity extension and field re-initialization techniques. In addition, a\nleast-squares smoothing technique is used to compute the local curvature of a\ngrain boundary directly from the level-set field without resorting to\nhigher-order interpolation. A notable feature is that the coupling between mass\ntransport, mechanics and grain-boundary migration is fully accounted for. The\ncomplexities associated with this coupling are highlighted and the\noperator-split algorithm used to solve the coupled equations is described.",
"arxiv_id": "physics/0411012",
"authors": [
"Hashem M. Mourad",
"Krishna Garikipati"
],
"categories": [
"physics.comp-ph"
],
"doi": "10.1016/j.cma.2006.06.005",
"journal_ref": "Comput. Methods Appl. Mech. Engrg., vol. 196, no. 1--3, pp.\n 595--607, 2006.",
"title": "Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics",
"url": "https://arxiv.org/abs/physics/0411012"
},
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