# Maximum-Entropy Based Estimates of Stress and Strain in Thermoelastic Random Heterogeneous Materials

Krause, Maximilian; Böhlke, Thomas

##### Abstract:
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 Kreher and Pompe (Internal Stresses in Heterogeneous Solids, Physical Research, vol. 9, 1989) 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 Al-Al$_{2}$O$_{3}$ composites is performed. ... mehr

 Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM) Publikationstyp Zeitschriftenaufsatz Publikationsjahr 2020 Sprache Englisch Identifikator ISSN: 0374-3535, 1573-2681 KITopen-ID: 1000122438 Erschienen in Journal of elasticity Verlag Springer Vorab online veröffentlicht am 23.07.2020 Nachgewiesen in Web of ScienceDimensionsScopus
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