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Equivalent continuum strain calculations based on 3D particle kinematic measurements of sand
Author(s) -
Amirrahmat Siavash,
Alshibli Khalid A.,
Jarrar Maha F.,
Zhang Boning,
Regueiro Richard A.
Publication year - 2018
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2779
Subject(s) - eulerian path , shearing (physics) , discrete element method , infinitesimal strain theory , granular material , finite element method , cauchy stress tensor , cauchy distribution , extended discrete element method , mechanics , solid mechanics , kinematics , continuum mechanics , shear (geology) , materials science , mathematics , classical mechanics , mathematical analysis , geotechnical engineering , physics , geology , structural engineering , engineering , mixed finite element method , composite material , finite element limit analysis , lagrangian
Summary Constitutive modeling of granular materials has been a subject of extensive research for many years. While the calculation of the Cauchy stress tensor using the discrete element method has been well established in the literature, the formulation and interpretation of the strain tensor are not as well documented. According to Bagi,[1][Bagi K, 1996] researchers mostly adopt well‐known continuum or discrete microstructural approaches to calculate strains within granular materials. However, neither of the 2 approaches can fully capture the behavior of granular materials. They are considered complementary to each other where each has its own strengths and limitations in solving granular‐mechanics problems. Zhang and Regueiro[2][Zhang B, 2015] proposed an equivalent continuum approach to calculating finite strain measures at the local level in granular materials subjected to large deformations. They used three‐dimensional discrete element method results to compare the proposed strains measures. This paper presents an experimental application of the Zhang and Regueiro[2][Zhang B, 2015] approach using three‐dimensional synchrotron microcomputed tomography images of a sheared Ottawa sand specimen. Invariant Eulerian finite strain measures were calculated for representative element volumes within the specimen. The spatial maps of Eulerian octahedral shear and volumetric strain were used to identify zones of intense shearing within the specimen and compared well with maps of incremental particle translation and rotation for the same specimen. The local Eulerian volumetric strain was compared to the global volumetric strains, which also can be considered as an averaging of all local Eulerian volumetric strains.