Axisymmetric Particle System Static Stress Analysis

As a kind of special soft condensed matter, Granular materials have many special properties and characteristics of motion. They represent both solid-like and liquid-like features, and exhibit rich phenomena of nonlinear dynamics. People have not formed uniform views and theories about these as yet.In recent years, granular matter has attracted significant attention from physicists, and become a rather active research field in soft matter physics. It is a fundamental question of granular physics that whether the classical theory of elasticity is valid for static granular matter or not. Granular solid has the capability to sustain static shear stress, moreover, if granular solid is slowly sheared, the elastic response is predominant. Both of these are similar to ordinary solids. From these we could conclude that the elastic theory mode is still suitable to static granular matter. Therefore, searching for an appropriate strain-stress relation or elastic energy expression is a main problem of granular statics analysis. Fortunately, our team has obtained an elastic energy expression and established a set of nonlinear elastic equations on granular matter based on indications of Hertz contact mechanics.In this paper, a strain-stress relation used for calculating static stress distributions in granular systems was deduced from nonlinear elastic theory, drawed a comparision with linear elastic theory, and discussed the nonlinear effect. Though this nonlinear elastic theory has successfully explained many special properties of granular matter, we need to study the theory from different aspects, especially know that whether it can give proper description about different geometric systems, so as to study its rationality and engineering value for application. Therefore, this paper designed a specific geometric device—Couette geometry specimen, and calculated the stress distribution based on granular elastic theory. The results show that both axial pressure and radial pressure gradually increased along with the increase of the inner barrel's torque M, which increased the lateral pressure coefficient. Actually, the result that the pressure increased along with the increase of shear stress as system's deformation was restricted reflects the shear dilatancy phenomenon of granular matter. Furthermore inner barrel's lateral pressure coefficient is larger than outer barrel's. The results also show that whether inner barrel's force F and torque M change or not, radial pressures are almost equal in the sample's boundaries, while axial pressures have several percent discrepancies between the boundaries. These nonlinear effects can be observed and measured by taking experiment directly, which are conducive to judge the rationality and limitation of granular elastic theory. Especially it depicts some nonlinear mechanical behavior. In addition, these research achievements provide a new calculating method for analyzing lateral pressure coefficient interested in soil engineering.