(339i) Yield Behavior of Dense Assemblies of Frictional Particles

A static granular assembly under shear yields when the shear stress reaches a critical value. Although the yield behavior of granular assemblies has been studied extensively and many yield functions have been proposed [e.g., see 1-3], the links to particle-level properties and direct measurements of microstructure evolution during yielding have not been fully established. In this poster presentation, we examine such connections between yield and the particle properties and microstructure evolution directly obtained from discrete element method (DEM) simulations.

To probe these connections, we have performed DEM simulations of dense granular assemblies subjected to triaxial compression and extension as well as shear deformation. We apply axisymmetric stress increments to initially isotropic assemblies under constant confining pressures using a stress-controlled procedure. The kinematics information at the continuum level is then obtained through statistical averaging. The assemblies are deemed to yield to flow when the continuous strain following a small stress increment exceeds 0.1. The simulations also afford detailed information about internal variables such as the fabric tensor and the coordination number of particles involved in force chains, which characterize the evolution of the microstructure of the assembly. Such simulations have been repeated at several different confining pressures and particle friction coefficients. These results are then analyzed to first identify the plastic deformation and then correlate the yielding behavior to microstructure evolution and particle properties.

The dependence of the shear stress to pressure ratio on shear strain reveals strain-hardening. This stress ratio is independent of pressure but increases with particle friction coefficient. The strain beyond which the assemblies yield to flow also increases with particle friction coefficient. The yield stress data from the three loading paths can all be fitted nicely using a Lade-Duncan type yield function [2], and to a lesser accuracy with a Drucker-Prager type yield function [1]. More importantly, we found that the strain hardening behavior is positively correlated to the anisotropy evolution, which is characterized by the second invariant of the fabric tensor. The center of the yield surface also translates in stress space as particle friction coefficient increases, which is consistent with experimental observations [4]. These results are then used to formulate a yield function in terms of particle friction coefficient, the coordination number and the fabric tensor. This yield function, coupled with associated flow rule and evolution equations for the microstructural quantities, describes quasi-static flow of dense granular assemblies.

References:

[1] D. C. Drucker and W. Prager. Soil mechanics and plastic analysis of limit design. Quarterly of Applied mathematics, 10:157?165, 1952.

[2] P. V. Lade and J. M. Duncan. Elastoplastic stress-strain theory for cohesionless soil. Journal of geotechnology engineering, 101:1037?1053, 1975.

[3] A. S. J. Suiker and N. A. Fleck. Frictional collapse of granular assemblies. Journal of Applied Mechanics, 71(3):350?358, 05 2004.

[4] P. V. Lade and M. K. Kim. Single hardening constitutive model for frictional materials: III. comparison with experimental data. Computers and Geotechnics, 6:31?47, 1988.