Macro- and micro-mechanical relationship of the anisotropic behaviour of a bonded ellipsoidal particle assembly in the elastic stage

• Published in: Acta geotechnica Vol. 16; no. 12; pp. 3899 - 3921
• Main Authors: Zhou, Zhi-hao, Wang, Hua-ning, Jiang, Ming-jing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021; Springer Nature B.V
• Subjects: Anisotropy; Assembly; Bonding; Civil engineering; Closed form solutions; Complex Fluids and Microfluidics; Composite materials; Constants; Deformation; Discrete element method; Elastic anisotropy; Elastic constants; Elastic properties; Energy balance; Engineering; Equivalence; Exact solutions; Foundations; Geoengineering; Geotechnical Engineering & Applied Earth Sciences; Granular materials; Hydraulics; Irregular particles; Mathematical analysis; Mechanics; Modulus of elasticity; Parameters; Particle shape; Poisson's ratio; Properties; Research methodology; Research Paper; Shear modulus; Simulation; Soft and Granular Matter; Soil Science & Conservation; Solid Mechanics; Strain; Stress-strain relationships; Three dimensional analysis; Ellipsoidal particle; Anisotropy; Distinct element method; Micropolar continuum
• ISSN: 1861-1125; 1861-1133
• DOI: 10.1007/s11440-021-01328-0

In this paper, we study analytically the three-dimensional (3D) stress–strain relationships at the elastic stage with regard to the anisotropic granular materials composed of regularly arranged bonded ellipsoidal particles by the micro-structural mechanics approach, where the macroscopic elastic constants are expressed in closed form with respect to the microscopic parameters. The bonded ellipsoidal particle assembly is first equivalent to a 3D lattice network composed of lattice beams with different contact properties. Based on the principle of energy balance, the macroscopic elastic stress–strain relationships for the equivalent micropolar continuum are obtained by analysing the unit cells of the lattice beam system. Using the proposed closed-form expressions of the anisotropic elastic constants, the elastic moduli, Poisson’s ratios, Cauchy and Cosserat shear moduli and bending moduli can be expressed as functions of the microscopic parameters pertaining to the particle shape, size and contact properties. The elastic moduli and Poisson’s ratios from closed-form expressions for regular particle arrangement and modified expressions for irregular particle arrangement are noted to be in agreement with the results obtained using distinct element method (DEM). The results suggest that the regularly arranged ellipsoid particle assembly shows a typical 3D orthotropic feature, and the elastic constants change significantly as the anisotropy of particle increases.