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Critical state and continuum plasticity theories have been used in research and engineering practice in soil and rock mechanics for decades. These theories rely on postulated relationships between material stresses and strains. Some classical postulates include coaxiality between stress and strain rates, stress–dilatancy relationships, and kinematic assumptions in shear bands. Although numerical and experimental data have quantified the strains and grain kinematics in such experiments, little data quantifying grain stresses are available. Here, we report the first-known grain stress and local strain measurements in triaxial compression tests on synthetic quartz sands using synchrotron X-ray tomography and 3D X-ray diffraction. We use these data to examine the micromechanics of shear banding, with a focus on coaxiality, stress-dilatancy, and kinematics within bands. Our results indicate the following: 1) elevated deviatoric stress, strain, and stress ratios in shear bands throughout experiments; 2) coaxial principal compressive stresses and strains throughout samples; 3) significant contraction along shear bands; 4) vanishing volumetric strain but nonvanishing stress fluctuations throughout samples at all stages of deformation. Our results provide some of the first-known in situ stress and strain measurements able to aid in critically evaluating postulates employed in continuum plasticity and strain localization theories for sands. 

{"Abstract":["Data used for the two-hour photoelasticity lesson on September 29, 2022 at the 2022 ALERT Doctoral School in Aussois, France.  <\/p>\n\nIn the Data directory, you will find the PEGS-master, PhotoelasticDisks, and Results subdirectories. You will also find the Jupyter notebook ALERTPhotoelasticity_220929_v1.ipynb.<\/p>\n\nPhotoelasticity data is in the PhotoelasticDisks subdirectory. N_Image and P_Image contain a sequence of images of 511 bidisperse birefringent disks in simple shear as viewed with unpolarized light and polarized light, respectively. The Positions subdirectory contains the position and radii of the disks in disks in each image. The G2images and radii_highlighted subdirectories contain, respectively: (1) images of each particle colored by G^2 as computed from the photoelasticity images via methods described in (Daniels, et al., Review of Scientific Instruments, 88, 051808 (2017)); (2) images of deformation of the particle with the outlines of each particle highlighted. Computations are performed in the accompanying ALERTPhotoelasticity_220929_v1.ipynb Jupyter notebook, which may be opened on any computer supporting jupyter notebooks or through Google Colab.<\/p>\n\nWithin PEGS-master, you can open PeGSDiskSolve.m to solve for inter-particle forces using methods described in Sec. V of (Daniels, et al., Review of Scientific Instruments, 88, 051808 (2017)) and in the thesis of James Puckett (thesis titled "State Variables in Granular Materials: an Investigation of Volume and Stress Fluctuations" and completed at North Carolina State University in 2012). You can also find a script titled "PlotExpVsSynth.m" that compares results from G^2 calculations; results are put into the Results subdirectory.<\/p>\n\nPaths may need to be changed in all scripts.<\/p>\n\nRelated content from the doctoral school can be found here: https://github.com/alert-geomaterials/2022-doctoral-school. <\/p>"]} 

We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and diffraction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.