Stochastic heterogeneity as fundamental basis for the design and evaluation of experiments

Abstract

This paper concerns the stochastic concept of heterogeneity of individual geometric descriptors of material properties. This allows defining the related concept of the representative volume/area element (RVE/RAE). A distinction is introduced between composition and configuration in geometric parameters, on the one hand, and structure-insensitivity and structure-sensitivity of material properties, on the other hand. Each configuration-sensitive geometric descriptor and each structure-sensitive material property will give rise to asymmetric probability density distributions for the relevant observations (on structure or property) obtained on equal-sized volume/area elements. The paper discusses the biased character of data averaged for engineering purposes when based on sub-representative samples. Nevertheless, sub-representative elements can still be employed for comparative studies in concrete technology, however under the strict conditions that the sizes of the sample and of the smallest observed structural elements are maintained as fixed proportions of the corresponding RVEs/RAEs. The implications of this underlying materials science concept are demonstrated in this paper by three illustrative examples dealing with cement-based materials.