Anisotropy is a quintessential property of granular materials, in large part stemming from the complex interparticle interactions modulated by particle shape, orientation, and contact properties. This paper delves into the microscopic underpinnings of elastic anisotropy within granular solids composed of non-spherical particles. Employing the Discrete Element Method (DEM), incremental probes have been imposed on packed configurations of ellipsoidal particles generated through a clumping strategy. The synthetic specimens were deliberately designed to prevent permanent rearrangements, thereby ensuring fully reversible granular structures. Through a comprehensive blend of analytical and numerical approaches, the study establishes scaling relationships that shed light on the intertwined influence of particle orientation and contact curvature on elastic anisotropy, effectively disentangling their individual contributions. The results enabled a clear mathematical identification of two coexisting forms of elastic anisotropy: one of microstructural type, stemming from the directional properties of the initial particle arrangement (which in an elastic context is here referred to as inherent) ) and another stemming from mechanical processes, such as contact interaction promoted by the imposed stress path (here referred to as induced). ). Specifically, it is found that each of these anisotropy contributions can be linked to distinct fabric variables, namely the shape fabric (here associated with particle orientation and aspect ratio of the particles) and the contact area fabric (here associated with the local normal force and curvature of the particles at contact points). Inherent elastic anisotropy is revealed to be predominantly governed by the microstructural characteristics of shape fabric, whereas, induced elastic anisotropy is shown to be primarily driven by the contact area fabric. By underscoring the critical role played by microstructural fabrics in determining macroscale elastic anisotropy, the DEM simulations also enabled the calibration of the fabric components of a nonlinear anisotropic hyperelastic model, thereby paving the way for enhanced predictive capabilities of constitutive laws for granular materials harnessing the profound connection between grain-scale processes and continuum-scale mechanical properties.

Standard laboratory tests, such as the triaxial test, are often considered to be element tests. But, when observing such a test, it becomes obvious that this assumption of homogeneity is far from accurate. The localisation of strain is often visible to the naked eye and becomes even more obvious when observed on the grain scale. Other variables, such as those describing the soil fabric, are expected to localise as well. In this work, two sand samples are analysed at different loading states regarding the heterogeneity of three soil variables: void ratio, coordination number and contact orientation anisotropy. For this purpose, the size of a Representative Elementary Volume (REV) is determined using three criteria: the convergence of the mean and variance of the variables with increasing element size as well as a chi(2)-test. The size of the REV is varying depending on the chosen variable but almost the same for the two specimens when related to the mean grain diameter d(50). The REV is placed in a regular grid throughout the specimen and the three variables are determined for each REV. The stochastic as well as spatial heterogeneity is identified for each specimen. As one of the samples is analysed for different loading states throughout a triaxial test, the evolution of the soil heterogeneity is identified. A localisation of all three variables can be observed at the end of the triaxial test as well as a strong initial heterogeneity for both sand samples.