A duality-based method for generating geometric representations of polycrystals
We present a method, which we have termed Relaxed Dual Complex (RDC), for generating geometric representations and computational models of polycrystals of arbitrary shape. The RDC method combines a first topological step, which defines an initial unrelaxed polycrystal geometry as the barycentric dual of an input triangulation of the solid, and a second relaxation step, in which the grain boundaries are relaxed by means of a gradient flow driven by grain boundary energy. The RDC method applies to arbitrary solids defined by means of a triangulation and, in this manner, it couples seamlessly to standard solid modelling engines. An additional appealing feature of the RDC method is that it generates a conforming tetrahedral mesh of the polycrystal that can be used as a basis for subsequent simulations. The RDC method also affords some control over the statistical properties of the polycrystal, including grain size, which provides a convenient device for matching experimental statistical data. The range, versatility, and performance of the RDC method have been demonstrated by means of selected examples.
© 2010 John Wiley & Sons, Ltd. Received 16 August 2010; Revised 15 October 2010; Accepted 20 October 2010. Article first published online: 28 Dec. 2010. The authors acknowledge the support of the United States Army Research office through the award: W911NF-06-0421 Mod/Amend#: P0001 and the support of the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials.