Title: A Generalized Finite Element Method for Polycrystals and Three-Dimensional Branched Discontinuities

Date/Time: Thursday, August 10, 2006, 10:00 – 11:00 am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: Micromechanical analysis of polycrystals using the classical finite element method (FEM) encounters several difficulties. The FEM requires the generation of meshes that fit the grain boundaries and are sufficiently refined in the neighborhood of singularities. The elements in a mesh must also have aspect ratios within acceptable bounds. In addition, uncertainty about, for example, grain morphology (size, size distribution and shape), requires the analysis of a very large number of models. This is a daunting task even in the case of two-dimensional models. In this talk, the generalized FEM (GFEM) for polycrystals recently proposed in [2] will be presented. In this approach, the FE mesh does not need to mimic the grain morphology since grain boundaries and junctions are described by means of discontinuous enrichment functions. The background GFEM used in the analysis can be refined as if there were no grains boundaries. This, combined with the proposed high-order GFEM approximations [1], provide a very flexible and robust method that can deliver accurate solutions.

Applications demonstrating the capabilities and potentialities of the proposed methodology are presented. Under appropriate loading conditions and temperature, grain boundary sliding is one of the main mechanism behind anelastic deformation of polycrystalline aggregates. We present a study on the effect of grain morphology on anelasticity of polycrystals caused by free grain boundary sliding. We carry out a series of simulations on a wide range of grain morphologies in several arrangements of grains.
The proposed GFEM can also be used for branched and intersecting cracks in two and three-dimensions. Three dimensional simulations demonstrating these capabilities are presented.

Finally, we discuss extensions of the method for the description of grain refinement, a phenomenon which is believed to be a key ingredient in the development of superplastic flow in some coarse-grained polycrystals.

References
[1] C. A. Duarte, L. G. Reno, and A. Simone. A three-dimensional generalized hp FEM for through-the-thickness branched cracks. In XVI Italian Conference on Computational Mechanics, Bologna, Italy, 26–28 June 2006. University of Bologna. 4 pages.
[2] A. Simone, C. A. Duarte, and E. van der Giessen. A generalized finite element method for polycrystals with discontinuous grain boundaries. International Journal for Numerical Methods in Engineering, 2006. In press.

CSRI POC: Thomas Voth, (505) 844-6004