Probability Distribution Of Contact Forces Research Articles

The effects of rolling resistance and non-convex particle on the mechanics of the undrained granular assembles in 2D

The rolling resistance at particle contacts and shape irregularity of particles are two major factors greatly influencing both the macroscopic and microscopic properties of granular assemblies. To study their influences on the mechanics of granular assembles under undrained tests, a rolling resistance model for two-dimensional disks and three types of non-convex grains (i.e. disk, ellipse and triangle) without rolling resistance are introduced into discrete element methods. Both macroscopic and microscopic responses are analyzed by consideration of four aspects of the mechanical quantities of these systems at the steady state, i.e. shear strength, solid fraction, force anisotropies, and probability distribution of contact forces, to analyze the influences of rolling resistance at particle contacts and shape irregularity of particles. Our main findings are: 1) the rolling resistance is unable to achieve as large critical shear strength of granular systems, even when the rolling resistance coefficient artificially becomes very large. 2) the main weight of anisotropic parameters which dominate the macroscopic shear strength for the non-convex particles is contact normal anisotropy, for the rolling resistance assembles is contact normal force anisotropy, and 3) the average friction mobilization for the rolling resistance assembles is much lower than that for the non-convex packings.

Non-Dissipative Structural Evolutions in Granular Materials

The structure of the contact network in granular assemblies can evolve due to either dissipative mechanisms such as sliding at contact points, or non-dissipative mechanisms through the phenomenon of contact gain and loss. Being associated with negligible deformations, non-dissipative mechanisms is actually active even in the small strain range of ~ 10−3 , especially in the case of densely packed assemblies. Hence, from a constitutive modelling point of view, it is crucial to be able to estimate such non-dissipative evolutions since both elastic and plastic properties of granular assemblies highly depend on contact network characteristics. The current study proposes an analytical scheme that allows us to estimate the non-dissipative contact gain/loss regime in terms of directional changes in the average contact force. The probability distribution of contact forces is used to compute the number of lost contact for each direction. Similarly, the number of newly formed contacts is estimated by considering the probability distribution of the gap between neighbouring particles. Based on the directional contact gain/loss computed, the changes in coordination number and fabric anisotropy can be found which, together with statistical treatments of Love-Weber stress expression, form a complete system of equations describing the evolution of other controlling microvariables. Finally, the results of the calculations have been compared with DEM simulations which verify the accuracy of the proposed scheme.

Numerical investigation on angle of repose and force network from granular pile in variable gravitational environments

This paper presents a numerical investigation on the relationship between the angle of repose and gravity by a three dimensional discrete element method. Taking particle shape, particle size and surface roughness of particle into account, the forming of granular pile was simulated under four different gravitational conditions: the Moon gravity, Martian gravity, Earth gravity and super-gravity. The angle of repose at macro level and the contact forces between particles of the pile were analyzed. Results show that the contact forces are lognormal distributed with about 65% smaller than the mean, and the ratio of tangential to normal force is uniformly distributed except for a small peak where the friction force is fully mobilized. The probability distribution of contact forces normalized by particle's weight under all gravity conditions shows to be in mutual coincidence, and the distribution of the ratio of tangential to normal force is independent of gravity. Although the microstructure of pile varies randomly, the angle of repose will not be affected by the magnitude of gravity.

Identification of rolling resistance as a shape parameter in sheared granular media

Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear conditions, we consider four aspects of the mechanical behavior of these systems in the steady state: shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. Our main finding is that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape.

Numerical study of the force network ensemble

The force network ensemble of Snoeijer et al. (Force network ensemble: a new approach to static granular matter, Phys. Rev. Lett. 92 (2004), 054302) is a convenient model to study networks of contact forces that are typically present in granular matter. Recently, we have shown that it is possible to extremely accurately determine the probability distribution of contact forces in the framework of this ensemble (van Eerd et al., Tail of the contact force distribution in static granular materials, Phys. Rev. E 75 (2007), 060302(R); Tighe et al., Entropy maximisation in the force network ensemble for granular solids, Phys. Rev. Lett. 100 (2008), 238001). In this work, we review several important details of these computations. In particular, we study in detail the angle-resolved contact force distribution, finite-size effects, the maximum allowed shear stress and the effect of walls. In addition, we investigate how well the force network ensemble resembles systems with ‘real’ interactions.

Sheared Force Networks: Anisotropies, Yielding, and Geometry

A scenario for the yielding of granular matter is presented by considering the ensemble of force networks for a given contact network and applied shear stress tau. As tau is increased, the probability distribution of contact forces becomes highly anisotropic, the difference between average contact forces along minor and major axes grows, and the allowed networks span a shrinking subspace of all force networks. Eventually, contacts start to break, and at the maximal shear stress the packing becomes effectively isostatic. The size of the allowed subspace exhibits simple scaling properties, which lead to a prediction for the yield stress for packings of an arbitrary contact number.