Constitutive relations for cohesionless frictional granular materials

Abstract

Based on the micro-mechanical model recently developed by Nemat-Nasser S. (J. Mech. Phys. Solids 48 (2000) 1541), a three-dimensional continuum mechanics model is presented for the deformation of granular materials which carry the applied load through frictional contacts. The model incorporates the anisotropy (or fabric) which develops as a frictional granular mass is deformed in shear, and includes the coupling between shearing and volumetric straining (or dilatancy). The model parameters are estimated, based on the results of a series of cyclic shearing experiments on large hollow cylindrical samples of silica sand. Then, the model is used to predict other experimental results, arriving at good correlation. #

Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials

“…Indeed for cellular and granular materials effective behavior laws are not available via homogenization procedures. For granular media the definition of a representative sample is still an open question and some homogenization procedures may be only applied to static behavior of granulates [10,11,32]; recall that a granular medium may behave as a solid or a fluid according to the external solicitations. The evolution of a granular medium is an erratic process with multiple possible paths, localization phenomena (shear bands) and local dynamic crisis (arching collapses).…”

Multi-mechanism anisotropic model for granular materials

“…The theory was largely guided by "shear" type tests (e.g., biaxial shear tests of Konishi et al, 1982 on rods, hollow cylindrical tests on sands, etc.). The theory has been shown to compare well with plane strain, and hollow-cylindrical test results (Zhu et al, 2006a;Nemat-Nasser and Zhang, 2002). Numerical triaxial simulations are provided in Balendran and Nemat-Nasser (1993), Zhu et al (2006a) and Nemat-Nasser and Zhang (2002).…”

“…The theory has been shown to compare well with plane strain, and hollow-cylindrical test results (Zhu et al, 2006a;Nemat-Nasser and Zhang, 2002). Numerical triaxial simulations are provided in Balendran and Nemat-Nasser (1993), Zhu et al (2006a) and Nemat-Nasser and Zhang (2002). In a recent paper, Zhu et al (2006c) compared the results from the doubleshearing theory with the results of a hypoplastic theory, verified using triaxial data, and showed good agreements.…”

The modeling of the shock response of powdered ceramic materials

“…There is a large body of research over the past several decades pertaining to the evaluation and modeling of compressive strength of brittle materials [12,15] and for oil shale, [5]. The pressure dependence of the compressive strength of brittle solids, such as rocks, stones, and concrete has been modeled through a wide variety of approaches.…”