Determination of a Representative Volume Element Based on the Variability of Mechanical Properties with Sample Size in Bread

Abstract

Quantitative analysis of food structure is commonly obtained by image analysis of a small portion of the material that may not be the representative of the whole sample. In order to quantify structural parameters (air cells) of 2 types of bread (bread and bagel) the concept of representative volume element (RVE) was employed. The RVE for bread, bagel, and gelatin-gel (used as control) was obtained from the relationship between sample size and the coefficient of variation, calculated from the apparent Young's modulus measured on 25 replicates. The RVE was obtained when the coefficient of variation for different sample sizes converged to a constant value. In the 2 types of bread tested, the tendency of the coefficient of variation was to decrease as the sample size increased, while in the homogeneous gelatin-gel, it remained always constant around 2.3% to 2.4%. The RVE resulted to be cubes with sides of 45 mm for bread, 20 mm for bagels, and 10 mm for gelatin-gel (smallest sample tested). The quantitative image analysis as well as visual observation demonstrated that bread presented the largest dispersion of air-cell sizes. Moreover, both the ratio of maximum air-cell area/image area and maximum air-cell height/image height were greater for bread (values of 0.05 and 0.30, respectively) than for bagels (0.03 and 0.20, respectively). Therefore, the size and the size variation of air cells present in the structure determined the size of the RVE. It was concluded that RVE is highly dependent on the heterogeneity of the structure of the types of baked products.