A modified micromorphic model based on micromechanics for granular materials

TL;DR

This paper introduces a modified micromorphic continuum model for granular materials, incorporating micromechanical insights to better capture the influence of particle translation and rotation on deformation behavior.

Contribution

It develops a novel micromorphic model based on micromechanics, considering particle translation and rotation, with simplified constitutive relationships for granular materials.

Findings

The model relates stress measures to symmetric and asymmetric strains.

Constitutive moduli incorporate microstructural contact stiffness and internal length.

The approach simplifies the micromorphic model by using first-order relationships.

Abstract

The purpose of this study is to propose a modified micromorphic continuum model for granular materials based on a micromechanics approach. In this model, Cauchy stress and the couple stress are symmetric conjugated with the symmetric strain and the symmetric curvature respectively, and the relative stress measures are asymmetric conjugated with the asymmetric relative strain measures. This modified micromorphic model considers a continuum material point as a granular volume element whose deformation behavior is influenced by the translation and the rotation of particles. And this study proposes that the microscopic actual motion is decomposed into a macroscopic motion and a fluctuation between the macro-micro motion. Based on this decomposition, the micromorphic constitutive relationships are derived for granular materials. In the constitutive relationships, the macroscopic constitutive relationships are first-order because of the introduce of the independent rotation of particle instead of the second-order micro-deformation gradient. Furthermore, the complex constitutive moduli in the micromorphic model are obtained in the expressions of the microstructural information such as the contact stiffness and the internal length.