From micro to macro: Creep behaviour and closed-form expression of viscoelastic parameters for a rheological particle assembly

Abstract

This study is devoted to analytically establish macro–micro quantitative relationships for creep characteristics of a rheological particle assembly, contributing to a more comprehensive insight into the interplay between different scales. To represent the various rheological behaviour in microscopic for a hexagonal close-packed (HCP) circular particle assembly, the contact responses are assumed as viscoelastic models. By extending the traditional homogenization method to the Laplace domain, the macroscopic one/two-dimensional creep equations of the rheological particle assembly, expressed with the microscopic contact parameters in a closed-form manner, are innovatively identified. It is found that the macroscopic creep behaviour is not always consistent with the microscopic one and in general exhibits more complex creep characteristics. The parametric analysis presents the quantitative influence of contact parameters on macroscopic creep behaviour. Extending the one-dimensional case to three dimensions (3D), the relaxation moduli as well as creep compliance, expressed in closed-form by contact parameters, are obtained in 3D viscoelastic constitutive equations. Distinct viscoelastic behaviours are observed for macroscopic shear and bulk responses. The proposed macro–micro quantitative relations of creep characteristics in this study benefit to deeply understand the macro–micro relations of viscoelastic properties, providing an alternative approach to calibrate microscopic parameters when involving the DEM simulations.