Abstract
A multi-scale model for the analysis of granular systems is proposed, which combines the principles of a coupled FEM–DEM approach with a novel servo-control methodology for the implementation of appropriate micro-scale boundary conditions. A mesh convergence study is performed, whereby the results of a quasi-static biaxial compression test are compared with those obtained by direct numerical simulations. The comparison demonstrates the capability of the multi-scale method to realistically capture the macro-scale response, even for macroscopic domains characterized by a relatively coarse mesh; this makes it possible to accurately analyse large-scale granular systems in a computationally efficient manner. The multi-scale framework is applied to study in a systematic manner the role of individual micro-structural characteristics on the effective macro-scale response. The effect of particle contact friction, particle rotation, and initial fabric anisotropy on the overall response is considered, as measured in terms of the evolution of the effective stress, the volumetric deformation, the average coordination number and the induced anisotropy. The trends observed are in accordance with notions from physics, and observations from experiments and other DEM simulations presented in the literature. Hence, it is concluded that the present framework provides an adequate tool for exploring the effect of micro-structural characteristics on the macroscopic response of large-scale granular structures.
Highlights
The intrinsic influence of the discrete micro-structure of granular materials on their effective material properties and structural response is nowadays well recognized
This is typically done by coupling the discrete element method (DEM), which accurately represents the complex particle behaviour at the micro scale [1,2,3,4,5,6,7,8,9,10], to the finite element method (FEM), B E
Coupled FEM– DEM approaches are commonly validated by analysing the macroscopic structural response in experimental tests typical for granular media, such as a biaxial compression test [11,15,17,18,19], a slope stability test [20], or a shear test [15]
Summary
The intrinsic influence of the discrete micro-structure of granular materials on their effective material properties and structural response is nowadays well recognized. In the current communication a novel multi-scale framework is presented for granular materials, which employs the formulation and implementation of the micro-scale boundary conditions recently published in [12]. This formulation is based on the first-order homogenization approach originally proposed in [11], which includes important aspects that are usually ignored in other homogenization methods for particle systems, namely (i) the Hill–Mandel micro-heterogeneity condition that enforces consistency of energy at the microand macro scales, (ii) the influence of particle rotations in the formulation of micro-to-macro scale transitions, and (iii) a rigorous generalization of the multi-scale relations within the theory of finite deformations. The dimensions related to volume, area, stress and mass density are consistently presented in their reduced form as length, length, force/length and mass/length, respectively
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