Origin of rigidity in dry granular solids.
Sumantra Sarkar1, Dapeng Bi, Jie Zhang
1Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
Physical Review Letters
|August 27, 2013
Summary
Shear rigidity in granular materials emerges collectively, controlled by boundary forces and force balance, not density changes. This rigidity is linked to broken translational symmetry in force space, observed in shear-jammed states.
Area of Science:
- Physics
- Materials Science
- Soft Matter Physics
Background:
- Solids resist shear, traditionally linked to broken translational symmetry and density variations.
- Dry granular materials challenge this paradigm, lacking preferred density modulations.
Purpose of the Study:
- Investigate the emergence of shear rigidity in granular solids.
- Develop a theoretical framework for rigidity in granular systems.
Main Methods:
- Formulated a theory based on boundary forces, force/torque balance, and positive contact forces.
- Applied the theory to experimentally generated shear-jammed states.
Main Results:
- Demonstrated that shear rigidity in granular materials is a collective process.
- Identified broken translational symmetry in force space, not position space, as key.
- Observed persistent, non-uniform force density modulation at the shear-jamming transition.
Conclusions:
- The emergence of shear rigidity in granular solids is governed by force network properties.
- The study redefines the link between rigidity and symmetry breaking in granular systems.
Related Concept Videos
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
01:11Alterations in Muscle Tone lll
Rigidity and myotonia are distinct abnormalities of muscle tone that affect resistance and relaxation during movement. Although both involve altered muscle contraction, they arise from different neurological and muscular mechanisms.CharacteristicsRigidity is characterized by uniform resistance to passive movement across the entire range, independent of speed, affecting flexors and extensors equally. It may appear as lead-pipe rigidity (smooth, constant resistance) or cogwheel rigidity...
01:21Polymer Classification: Crystallinity
Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
01:12Temperature Dependent Deformation
In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...
01:22Generalized Hooke's Law
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
01:26Hooke's Law
Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.