We present a numerical methodology for the thermomechanical analysis of real polycrystalline material microstructures obtained using electron backscatter di¤raction techniques. The asymptotic expansion homogenization method is used in conjunction with the …nite element method to perform comprehensive micromechanical analyses and determine the e¤ective thermoelastic properties of polycrystalline materials. Smooth grain boundaries are generated from the discretely sampled electron backscatter di¤raction data of real polycrystalline materials. The microscale displacements, strains and stresses are related to the macroscale temperature change and strains through 21 distinct characteristic functions. The three-dimensional equilibrium equations at the microscale yield a system of partial di¤erential equations for the characteristic functions which are solved using the …nite element method. The e¤ective properties of the polycrystalline material are obtained from the single-crystal thermoelastic properties, crystallographic orientations of the crystallites and the characteristic functions. The proposed methodology is demonstrated by considering electron backscatter di¤raction maps of zinc, stainless steel, and natural quartzite rock. Results are presented for homogenized properties such as elastic sti¤nesses, thermal expansion coe¢ cients, and seismic wavespeeds, as well as for microscale stress distributions resulting from di¤erent macroscale loading conditions. The bulk thermoelastic properties are compared with those obtained using the Voigt, Reuss, Voigt-Reuss-Hill and self-consistent methods. Details are provided regarding a freely available software package that has been developed for the thermomechanical analysis of polycrystalline materials based on the proposed numerical framework.

The constitutive laws of polyphase aggregates dominantly depend on the operative deformation mechanisms, phase morphology and modes, and environmental conditions. Each of these factors has the potential to dramatically affect bulk mechanical properties as well as the local stress and strain rate distributions. To focus on the effects of phase morphology, we have developed a rigorous multiscale approach based on asymptotic expansion homogenization. The proposed methodology has two fundamental goals: (1) accurately predict bulk behavior in aggregates by explicitly taking into account phase morphology and (2) calculate detailed distributions of strain rates, stresses, and viscosities in heterogeneous materials. The methodology is able to consider general nonlinear phase constitutive laws that relate strain rates to stresses, temperature, and other factors such as water fugacity and grain size. We demonstrate the approach by analyzing power law creep of computer-generated and natural polyphase systems and benchmarking the results against analytical solutions. As an outcome of this analysis, we find that the approximation of an aggregate as a power law material is reasonable for isotropic, homogeneous phase distributions but breaks down significantly with high degrees of phase organization. We also present distributions in strain rate, stress, and viscosity for different applied loading conditions. Results exhibit areas of high internal stresses and substantial localization. We describe and provide a freely available software package supporting these calculations.

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