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Large deformation granular strain measures and calculations of granular stress based upon 3-dimensional ellipsoidal dem

Seven finite strain measures for granular materials are developed based on three-dimensional (3D) discrete element (DE) simulations: two are calculated in the reference configuration, and the other five are calculated in the current configuration. The difficulty in calculating strain measures for granular materials is the discrete particulate nature of the materials. The seven strain measures are motivated by the equivalent continuum method, but are extended to finite strain in 3D. Simulations are conducted to test the finite strain measures, and it is found that the seven finite strain measures are independent of rigid body rotation of a particle assembly. Granular stress is also calculated to be able to plot stress-strain curves.
Finally, two numerical examples with large deformation are simulated: (1) cavity expansion, and (2) pile penetration; and their results are analyzed.

Author(s):

Boning Zhang    
University of Colorado, Boulder
United States

Richard Regueiro    
University of Colorado, Boulder
United States