Connecting discrete particle mechanics to continuum granular micromechanics: Anisotropic continuum properties under compaction

Abstract

A systematic and mechanistic connection between granular materials macroscopic and grain level behaviors is developed for monodisperse systems of spherical elastic particles under die compaction. The Granular Micromechanics Approach (GMA) with static assumption is used to derive the stiffness tensor of transversely isotropic materials, from the average behavior of particle-particle interactions in all different directions at the microscale. Two particle-scale directional density distribution functions, namely the directional distribution of a combined mechanogeometrical property and the directional distribution of a purely geometrical property, are proposed and parametrized by five independent parameters. Five independent components of the symmetrized tangent stiffness tensor are also determined from discrete particle mechanics (PMA) calculations of nine perturbations around points of the loading path. Finally, optimal values for these five GMA parameters were obtained by minimizing the error between PMA calculations and GMA closed-form predictions of stiffness tensor during the compaction process. The results show that GMA with static assumption is effective at capturing the anisotropic evolution of microstructure during loading, even without describing contacts independently but rather accounting for them in an average sense.

A New Combined Model for considering the Plasticity Effects in Contacting Asperities

“…P k (cosφ) is the k th order Legendre polynomial with respect to cosφ, 4 Mathematical Problems in Engineering polynomials P 2 and P 1 2 are matched to the single asperity contact problem which we assumed at the beginning to simplify equation (9). According to Poorsolhjouy and Gonzalez [23], parameter a20 is equal to −0.5 in a wide range of density values. Furthermore, we assume parameters a 21 and b 21 are equal to 1 because the shape of the distribution function for the azimuthal angles is harmonic in the asperities contact zone.…”

A review of continuum damage and plasticity in concrete: Part II – Numerical framework

“…The localization, interaction between microcracks, and scale effects are difficult to capture with standard FEM, therefore, Rossi Cabral et al (2019) proposed a bilinear peridynamic approach for quasibrittle material by discrete element method. Several ways using DEM, peridynamic approaches, coupled discrete particle mechanics-continuum mechanics are presented in the literature (Da Silva et al, 2020;Nguyen et al, 2019;Picandet et al, 2016;Poorsolhjouy and Gonzalez, 2018;Puglia et al, 2019).…”

Generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength

“…We specifically study the orientation distribution function of contact normals and of the mean contact force. Using spherical coordinates with azimuth and zenith angles θ and φ, we define the contact orientation vector by n = (sin(θ) cos(φ), sin(θ) sin(φ), cos(θ)) and, for axial symmetry around the zenith axis or the direction of compaction [65], the spherical harmonics spectrum of the orientation distribution function of contact normals ξ(n) = ξ(θ, φ) [ Figures 17 and 18 show the orientation distribution function of the mean contact force and of contact normals after compaction, unloading and ejection obtained from the particle contact mechanics simulation of the granular bed at relative densities ρ in-die max equal to 0.7323 and 0.9950, respectively. It is evident from the figure that: (i) the small number of large forces are oriented in the loading direction after compaction, while the large number of intermediate to small forces are oriented at ±60 • from the loading direction; (ii) the orientation distribution of contact normals does not significantly change during unloading and ejection due to the plastic, permanent nature of the deformations; (iii) after unloading, most large, vertically oriented forces are relaxed and, after ejection, most radially oriented forces are relaxed; (iv) compressive residual forces in the ejected solid compact are mostly oriented at ±60 • from the loading direction, and there is a small number of tensile residual forces that are oriented in the direction of loading; and (v) the orientation distribution of residual mean contact forces is different for different relative densities ρ in-die max .…”

“…In this section, for simplicity, we assume isotropic behavior and thus determine two elastic properties, i.e., Young's modulus and Poisson's ratio, from the unloading curve. This assumption can be relaxed and, if a transversely isotropic material is assumed, five anisotropic continuum properties can be determined from the loading curve [65]. The extension of this analysis to unloading and ejection stages, though beyond the scope of this work, is currently being pursued by the author.…”