Force chain buckling, unjamming transitions and shear banding in dense granular assemblies

• Published in: Philosophical magazine (Abingdon, England) Vol. 87; no. 32; pp. 4987 - 5016
• Main Author: Tordesillas, A.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 11.11.2007; Taylor and Francis
• Subjects: Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Deformation and plasticity (including yield, ductility, and superplasticity); Exact sciences and technology; Materials science; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Physics; Porous materials; granular materials; Specific materials; Potential energy; Constitutive equation; Deformation; Structure stability; Strain softening; Strain energy; Mechanical properties; Shear strength; Granular structure; Energy relaxation; Spatial distribution; Stress distribution; Strong correlation; Energy dissipation; Granular materials; Dimensional analysis; Shear stress; Strain distribution; Stress effects; Internal variable material; Kinetic energy; Shear band; Buckling
• ISSN: 1478-6435; 1478-6443
• DOI: 10.1080/14786430701594848

Force chain buckling, leading to unjamming and shear banding, is examined quantitatively via a discrete element analysis of a two-dimensional, densely-packed, cohesionless granular assembly subject to quasistatic, boundary-driven biaxial compression. A range of properties associated with the confined buckling of force chains has been established, including: degree of buckling, buckling modes, spatial and strain evolution distributions, and relative contributions to non-affine deformation, dilatation and decrease in macroscopic shear strength and potential energy. Consecutive cycles of unjamming-jamming events, akin to slip-stick events arising in other granular systems, characterize the strain-softening regime and the shear band evolution. Peaks in the dissipation rate, kinetic energy and local non-affine strain are strongly correlated: the largest peaks coincide with each unjamming event that is evident in the concurrent drops in the macroscopic shear stress and potential energy. Unjamming nucleates from the buckling of a few force chains within a small region inside the band. A specific mode of force chain buckling, prevalent in and confined to the shear band, leads to above-average levels of local non-affine strain and release of potential energy during unjamming. Ongoing studies of this and other buckling modes from a structural stability standpoint serve as the basis for the formulation of internal variables and associated evolution laws, central to the development of thermomicromechanical constitutive theory for granular materials.