Experimental Characterization of Spatial Randomness of Elastic Properties of Heterogeneous Materials

Background: Understanding the stochastic nature of elastic constants is crucial for the probabilistic analysis of structural response. Although significant progress has been made in experimentally characterizing deformation fields, few studies have addressed the spatial variability of material properties. Objective: This study aims to develop a robust numerical-experimental method for characterizing the statistics of the elastic constants of heterogeneous materials. Methods: The proposed method integrates digital image correlation (DIC) with finite element (FE) analysis. Through an iterative matching process between DIC-measured strain fields and FE simulations, the random spatial distributions of elastic constants are identified. This information is then used to determine the probability distributions, spatial autocorrelation functions, and cross-correlation functions of the elastic constants. Results: The method is applied to microcrystalline cellulose tablets subjected to diametral compression. The experimental results highlight the influence of compaction pressure on the statistical characteristics of the elastic constants. The analysis also uncovers key methodological considerations, including the DIC measurement noise, applied load level, matching region selection, and DIC resolution. Conclusions: The study demonstrates that the spatial distribution of elastic constants of heterogenous materials can be determined by optimal fitting of DIC-measured strain fields with those from elastic FE analysis. The resulting probability distribution and spatial correlation can be directly employed to generate the random fields of elastic properties for stochastic FE simulations.