BULK AND MICROSCALE RHEOLOGICAL PROPERTIES OF POLYPHASE POWER-LAW MATERIALS

We present here a new numerical tool for calculating the homogenized and microscale properties of polyphase power-law materials. A MATLAB-based graphical interface allows the user to import graphics files as well as electron backscatter diffraction datasets. The user then provides the power-law constants for each phase and defines the parameters of the analysis. Calculations are based on asymptotic expansion homogenization (AEH), which explicitly accounts for grain-to-grain interactions. In 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. Calculation results include bulk power-law properties as determined near the isoviscous point for a given temperature range, and microscale distributions of stress, strain-rate, and viscosity.

We demonstrate that (a) a power-law relationship satisfactorily describes a the bulk properties of a composite comprising two power-law materials, (b) the strength of many natural deep crustal rocks lies approximately midway between the theoretical strength bounds, and (c) microscale stress distributions can significantly affect microstructural development. We have applied variants of this method to calculate elastic properties, thermal conductivity, thermal expansion, and microfracturing.