Force, relative-displacement, and work networks in granular materials subjected to quasistatic deformation

To describe the heterogeneous nature of stress transmission in granular materials, the concept of the “strong” network consisting of contacts with large normal forces has been proposed by Radjaï et al. [Phys. Rev. Lett. 80, 61 (1998)]. The shear stress is mainly determined by this strong network. The dual viewpoint is adopted here, by not only considering the forces at contacts, but also the deformation. It is shown that the strain increments are determined by the tangential component of the relative displacements at the contacts. A “mobile” network consisting of contacts with large tangential relative displacements is defined that primarily accounts for the strain increments. The investigation of the relation between the strong and the mobile networks shows that these networks are largely unrelated. An alternative network is defined that consists of contacts at which the contribution to the work input is large. It is found that this work input occurs primarily through the tangential forces and tangential relative displacements.

Figure 1

(Color online) Macroscopic response: evolution with imposed strain ${ϵ}_1$ of shear strength $q∕p$ and volumetric strain ${ϵ}_V$.

Figure 2

(Color online) Partial pressure $p\left(\alpha \right)$ and partial shear stress $q\left(\alpha \right)$ at peak shear strength (top) and at large strain (bottom).

Figure 3

(Color online) Evolution with imposed strain ${ϵ}_1$ of contributions due to normal and tangential relative displacements to volumetric strain increment (top) and shear strain increment (bottom).

Figure 4

(Color online) Partial volumetric and strain increment $d{ϵ}_V\left(\beta \right)$ and partial shear strain increment $d{ϵ}_S\left(\beta \right)$ at peak shear strength (top) and at large strain (bottom).

Figure 5

(Color online) Force and relative-displacement networks for part of the assembly. The color of the contacts signifies the type of contact: red contacts are strong and mobile; green contacts are strong and immobile; blue contacts are weak and mobile; and black contacts are weak and immobile. Result at peak shear strength; $\alpha =\beta =0.8$.

Figure 6

(Color online) Evolution with imposed strain ${ϵ}_1$ of contributions to the work increments of the normal and tangential modes, $\delta W^N$ and $\delta W^T$, respectively; ${\sigma }_0$ is the initial isotropic stress.

Figure 7

(Color online) Partial work increment at peak shear strength.