Oscillatory instabilities in three-dimensional frictional granular matter

Area of Science:

• Physics
• Materials Science
• Mechanical Engineering

Background:

• Amorphous granular matter with friction lacks Hamiltonian derivation, leading to known oscillatory instabilities in 1D and 2D systems.
• The behavior of three-dimensional (3D) granular systems exhibiting these instabilities remained largely unstudied.

Purpose of the Study:

• To investigate and demonstrate the presence of oscillatory instabilities in 3D granular packing.
• To analyze the dynamics and consequences of these instabilities in a 3D context.

Main Methods:

• Studied binary assemblies of spheres with two distinct sizes.
• Employed classical Hertz and Mindlin force laws for longitudinal and tangent interactions, respectively.
• Analytically formulated the stability matrix in three dimensions.

Main Results:

• Confirmed the emergence of complex eigenvalues in the 3D stability matrix, analogous to 2D frictional disk systems.
• Observed oscillatory exponential growth in the mean-square displacement of the granular matter.
• Documented catastrophic events involving significant loss of mechanical stress and energy.

Conclusions:

• Oscillatory instabilities are present in 3D granular packings, similar to lower dimensions.
• These instabilities can lead to sudden, catastrophic energy and stress dissipation in granular systems.
• The findings are general for forces breaking Hamiltonian symmetry in granular matter.