Thermodynamically consistent fabric tensor definition from DEM to continuum

In elastoplastic soil constitutive models aimed at capturing the impact of anisotropy, a necessary ingredient is a tensor valued internal variable referred to as fabric tensor. Such fabric tensor and its evolution are traditionally defined based on indirect macroscopic observations at the continuum level, but the recent development in particle mechanics has made it possible to define the fabric tensor based on direct microstructural observations, which is potentially more effective and insightful. These microstructural observations are usually made by use of DEM, such as those related to interparticle contact normal directions. However, direct adaptation of DEM-based fabric tensor to elastoplastic modeling carries the risk of violating fundamental thermodynamic requirements. This is because the evolution of a fabric tensor in elastoplastic modeling must be properly linked to physical per volume dissipation. Consequently the continuum fabric tensor is necessarily an extensive quantity measured per unit volume, with a thermodynamically conjugate intensive force. This pervolume trait is not usually granted by a DEM constructed fabric tensor. It is therefore necessary to carefully consider the thermodynamic consistency when adapting DEM observations and measurements to elastoplastic modeling and continuum constitutive theories. The present work addresses this issue, brings up possible pitfalls if such consistency is violated and proposes guidelines for such adaptation.