Compression and reconstruction of random microstructures using accelerated lineal path function

Abstract Microstructure reconstruction and compression techniques are designed to identify microstructures with desired properties. While a microstructure reconstruction involves searching for a microstructure with prescribed statistical properties, a microstructure compression focuses on efficient representation of material morphology for the purpose of multiscale modelling. Successful application of these techniques, nevertheless, requires proper understanding of the underlying statistical descriptors quantifying morphology of a material. In this paper, we focus on a lineal path function designed to capture short-range effects and phase connectedness, which can hardly be handled by the commonly used two-point probability function. Usage of the lineal path function is, however, significantly limited because of huge computational requirements. So as to examine the properties of the lineal path function during computationally exhaustive compression and reconstruction processes, we start with an acceleration of the lineal path evaluation, namely by porting part of its code to a graphics processing unit using the CUDA (Compute Unified Device Architecture) programming environment. This allows us to present a unique comparison of the entire lineal path function with the commonly used rough approximation based on the Monte Carlo and/or sampling template. Moreover, this accelerated version of the lineal path function is then compared to the two-point probability function during the compression and reconstruction of two-phase morphologies. Their significant features are discussed and illustrated using a set of artificial periodic as well as real-world random microstructures.