Paper No. 1
Presentation Time: 8:00 AM
INTEGRATED ANALYTICAL-COMPUTATIONAL FRAMEWORK FOR THE CALCULATION OF BULK ELASTIC PROPERTIES AND SEISMIC WAVE SPEEDS IN POLYCRYSTALLINE MATERIALS
VEL, Senthil S.1, JOHNSON, Scott E.
2, COOK, Alden C.
1, GOUPEE, Andrew J.
1, SONG, Won Joon
3 and OKAYA, David
4, (1)Department of Mechanical Engineering, University of Maine, Orono, ME 04469-5711, (2)Department of Earth Sciences, University of Maine, 5790 Bryand Global Sciences, Orono, ME 04469, (3)Department of Earth Sciences, University of Maine, Orono, ME 04469, (4)Dept. Earth Sciences, University of Southern California, Los Angeles, CA 90089-0740, senthil.vel@maine.edu
The calculation of bulk elastic stiffnesses of rocks from microstructural information is important in a variety of applications. The Voigt and Reuss bounds give the maximum and minimum possible values, respectively, given only two parameters, namely the modal mineralogy and crystallographic orientations of the minerals. Where the true property lies between these two bounds is determined by the spatial arrangements, shapes, sizes, and shape orientations of the grains. Various averages that lie between the two bounds have been proposed, including the Voigt-Reuss-Hill average and the geometric mean. Although these averages closely approximate laboratory-determined bulk properties in some instances, they lack physical justification. Rigorous theoretical methods, such as the self-consistent and differential effective medium methods, consider the interaction of each individual grain with an effective background material, but do not explicitly account for the intra-grain heterogeneous stress fields that arise from grain-scale interactions.
We present a versatile computational method for the calculation of bulk properties which takes into account the grain-scale interactions (Naus-Thijssen et al., 2011). In this approach, known as asymptotic expansion homogenization (AEH), the heterogeneous microscale displacement fluctuations are related to the corresponding average macroscale strains via characteristic functions that are evaluated using the finite element method. The resulting bulk elastic properties, which are obtained using the characteristic functions, have first-order correlation to all microstructural features including the size, shape, crystallographic orientation and spatial arrangement of the grains. We show how the method can be integrated with electron backscatter diffraction (EBSD) data from natural rocks, as well as computer-generated (synthetic) microstructures, and present computational tools for evaluating the bulk elastic stiffnesses and seismic anisotropy of rock samples, as well as bulk thermal conductivities and thermal expansions.
References:
Naus-Thijssen, F. M. J., Goupee, A. J., Vel, S. S., Johnson, S. E., 2011. Geophysical Journal International, 185: 609–621. doi: 10.1111/j.1365-246X.2011.04978.x
