Deciphering how the particle shape modulates the elastic anisotropy of granular media

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.