pp 1–18 | Cite as

Numerical simulations of granular material behavior under rotation of principal stresses: micromechanical observation and energy consideration

  • Q. X. Wu
  • Z. X. YangEmail author
  • X. Li
Progress in Mechanics of Soils and General Granular Flows


A numerical investigation on the behavior of granular materials subjected to the rotation of principal stresses using the discrete element method is presented. A numerical procedure is developed to implement the two-dimensional arbitrary stress or strain paths imposed on polygonal specimens. Significant volumetric strain can be obtained and granular assembly appears to develop an anisotropic internal structure characterized by the contact-normal-based fabric tensor in due course, with its direction being rotated with the rotation of the principal stress. The observations indicate a significant degree of non-coaxiality between the principal-stress direction and the principal-strain increment direction. An ultimate state can be reached after sufficiently large numbers of cycling, resulting in a constant fabric norm and a circular strain trajectory in the deviatoric space. The boundary work, dissipation, and strain energy, are also registered during the entire loading process and its correlation between non-coaxial deformations is analyzed from micro-scale perspective. Before the ultimate state is reached, the applied work is partially dissipated by frictional sliding, and the remainder is stored as the strain energy within the specimen. When the ultimate state is reached, however, no change in the strain energy is obtained, and the plastic work is entirely dissipated, as the elastic portion of the free energy increment only depends on the elastic strain.


Discrete element method Granular material Principal-stress rotation Fabric evolution Energy dissipation Noncoaxiality 



The research described was funded by the Natural Science Foundation of China (Grant Nos. 51825803, 51578499, and 51609179), the National Key Basic Research Program of China (No. 2015CB057801), and Project of Thousand Youth Talents (No. 51078068).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringZhejiang UniversityHangzhouChina
  2. 2.School of Civil EngineeringSoutheast UniversityNanjingChina

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