A maximum entropy approach for property prediction of random microstructures

The task of reconstruction of microstructures from their limited description is posed as a maximum entropy (MaxEnt) problem. Microstructural descriptors are taken in the form of volume fractions, correlation functions and grain sizes. Morphological and size quantifications are used as features of microstructures and samples consistent with these features are reconstructed. The non-uniqueness of the reconstructed distribution is effectively encountered by choosing the distribution with the maximum entropy. Properties of random microstructures are characterized statistically using the MaxEnt solution. Microstructures reconstructed from correlation measures are interrogated to obtain elastic properties. For estimating plastic property statistics, grain size and orientation distribution information are incorporated. Analysis of plastic properties is performed in two steps, firstly by reconstructing microstructures with macro-specifications of grain size and secondly by attributing an orientation to each grain drawn from the MaxEnt distribution of the orientation distribution function (ODF). The MaxEnt ODF distribution is obtained by constraining the expected ODF over a sufficiently large number of microstructure samples to match with the given ODF information. Further, the effect of incorporating a larger amount of information on the variation of the effective behavior is studied. Numerical examples demonstrating the method for one- and two-dimensional microstructures are discussed.