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Maximum-entropy based estimates of stress and strain in thermoelastic random heterogeneous materials. (English) Zbl 1448.74025

Summary: Mean-field methods are a common procedure for characterizing random heterogeneous materials. However, they typically provide only mean stresses and strains, which do not always allow predictions of failure in the phases since exact localization of these stresses and strains requires exact microscopic knowledge of the microstructures involved, which is generally not available. In this work, the maximum entropy method pioneered by W. Kreher and W. Pompe [Internal stresses in heterogeneous solids. Berlin: Akademie-Verlag GmbH (1989; Zbl 0760.73001)] is used for estimating one-point probability distributions of local stresses and strains for various classes of materials without requiring microstructural information beyond the volume fractions. This approach yields analytical formulae for mean values and variances of stresses or strains of general heterogeneous linear thermoelastic materials as well as various special cases of this material class. Of these, the formulae for discrete-phase materials and the formulae for polycrystals in terms of their orientation distribution functions are novel. To illustrate the theory, a parametric study based on \(\text{Al-Al}_2 \text O_3\) composites is performed. Polycrystalline copper is considered as an additional example. Through comparison with full-field simulations, the method is found to be particularly suited for polycrystals and materials with elastic contrasts of up to 5. We see that, for increasing contrast, the dependence of our estimates on the particular microstructures is increasing, as well.

MSC:

74E05 Inhomogeneity in solid mechanics
74F05 Thermal effects in solid mechanics
74B05 Classical linear elasticity
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics

Citations:

Zbl 0760.73001

Software:

FFTW; FFTHomPy
PDFBibTeX XMLCite
Full Text: DOI

References:

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