Statistical Volume Elements (SVEs) are used to homogenize apparent elastic and fracture properties of material at length scales smaller than commonly used Representative Volume Elements (RVEs). Two of the key consequences are maintaining inherent material heterogeneity and sample-to-sample variations. These aspects are specifically important to capture certain key features of brittle fracture when, instead of computationally expensive Direct Numerical Simulation (DNS), upscaled and homogenized material properties are used in the context of a numerical homogenization scheme.
Advances in additive manufacturing have paved the way to print novel ceramic composites. For example, recent successes in printing of distinct layers and phases of silicon carbide and boron carbide can result in novel mechanical properties. We will use a set of experimental images of the microstructure of 3D printed ceramics to extract 2D SVEs at different observation sizes. By using static and dynamic simulations, elastic and fracture properties of the SVEs are obtained. We will perform various statistical analyses on these mesoscopically homogenized fields. For example, the effect of SVE size on heterogeneity, anisotropy of elasticity, and fracture properties will be discussed. Moreover, we will relate microstructural descriptors such as volume fraction and inherent length scales of various phases of the printed materials to mesoscopically homogenized properties.
