Vibrations of jammed disk packings with Hertzian interactions

Contact breaking and Hertzian interactions between grains can both give rise to nonlinear vibrational response of static granular packings. We perform molecular dynamics simulations at constant energy in 2D of frictionless bidisperse disks that interact via Hertzian spring potentials as a function of energy and measure directly the vibrational response from the Fourier transform of the velocity autocorrelation function. We compare the measured vibrational response of static packings near jamming onset to that obtained from the eigenvalues of the dynamical matrix to determine the temperature abovewhich the harmonic approximation breaks down. We compare packings that interact via single-sided (purely repulsive) and double-sided Hertzian spring interactions to disentangle the effects of the shape of the potential from contact breaking. Our studies show that while Hertzian interactions lead to weak nonlinearities in the vibrational behavior (e.g. the generation of harmonics of the eigenfrequencies of the dynamical matrix), the vibrational response of static packingswithHertzian contact interactions is dominated near jamming by contact breaking as found for systems with repulsive linear spring interactions. C. F. Schreck · C. S. O’Hern (B) · M. D. Shattuck Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520-8260, USA e-mail: [email protected] C. F. Schreck · C. S. O’Hern Department of Physics, Yale University, New Haven, CT 06520-8120, USA C. S. O’Hern Department of Applied Physics, Yale University, New Haven, CT 06520-8120, USA M. D. Shattuck Physics Department, Benjamin Levich Institute, The City College of the City University of New York, New York, NY 10031, USA