# A Micromechanics-Based Anisotropic Constitutive Model for Sand Incorporating the True Stress Tensor

## TL;DR

This paper introduces a new model for sand behavior that accounts for microscopic particle interactions and accurately predicts macroscopic deformation and strength.

## Contribution

A novel micromechanics-based constitutive model for sand incorporating true stress tensor and anisotropic fabric evolution.

## Key findings

- The model accurately captures stress–strain and volumetric deformation under conventional loading.
- It predicts strength dependency on loading direction and behavior under complex stress paths.
- Validation with triaxial tests and simulations confirms the model's universality and validity.

## Abstract

To elucidate the micromechanical origins of the macroscopic anisotropic behavior of granular materials, this study develops a micromechanically based elastoplastic constitutive model for sand. First, anchored in the static equilibrium hypothesis and granular micromechanics theory, a true stress tensor is introduced to characterize the authentic inter-particle contact forces. Serving as a coupled variable of the macroscopic stress and the microscopic fabric tensor, this formulation not only quantifies the directional distribution of the contact network but also enables the mapping of anisotropic yielding and deformation analyses into an equivalent isotropic true stress space. Subsequently, a comprehensive constitutive framework is established by integrating critical state theory, an anisotropic fabric evolution law, and an energy-based stress–dilatancy relationship that explicitly accounts for the evolution mechanism of the microscopic coordination number. The physical interpretation, calibration procedure, and sensitivity analysis of the model parameters are also presented. The predictive capability of the model is rigorously validated against conventional triaxial tests on Ottawa sand, true triaxial numerical simulations, and experimental data for Toyoura sand with inherent anisotropy. The comparisons demonstrate that the model accurately captures not only the stress–strain response and volumetric deformation under conventional loading but also the strength dependency on loading direction and mechanical characteristics under complex stress paths, substantiating the validity and universality of the proposed micromechanical approach.