In this talk, I present a summary of studies on the impact of a projectile in dense suspensions, based on published papers that theoretically and experimentally [1-4].
In the first part, I focus on the early-stage dynamics of the impact, which the floating model can describe without consideration of the elastic force acting on a projectile [2,4].
In the second part, I discuss how the...
Several mean-field theories predict that the Hessian matrix of amorphous solids converges to the Wishart matrix in the limit of large spatial dimensions. Motivated by these results, we calculate here the density of states of random packing of harmonic spheres by mapping the Hessian of the original system to the Wishart matrix. We compare our result with that of previous numerical simulations...
We performed a weeknonlinear analysis of particle configurations exhibiting negative eigenvalues in the Hessian matrix. By expanding the potential energy with respect to particle displacements, we found that the linear term enhances the instability, while the cubic term suppresses its growth. A comparison between the derived nonlinear equation and numerical simulations revealed qualitative...
We formulate the kinetic theory of dry granular particles under a simple shear based on the Enskog and Grad approximations. We get a complete set of equations for the kinetic stress and the collisional contribution to the stress within this approximation. The steady solution under this approximation reproduces the quantitatively accurate results for the shear viscosity and kinetic temperature...
We numerically investigate the shear modulus of jammed amorphous solids composed of cohesive grains. While repulsive grains exhibit critical scaling of the shear modulus as a function of the pressure or the excess coordination number, cohesive grains show pronounced hysteresis, which obscures the scaling behavior observed in repulsive systems. We relate this deviation to a possible breakdown...
Many structures around us achieve mechanical stability against their
own weight through friction. Examples include arch bridges,
house-of-cards construction, and sandpile stabilized by their angle
of repose. In these systems, friction and geometry work together
to suppress sliding and enables mechanical equilibrium. But what
(if any) mechanism contributes to the strength of...
When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of...
The jamming transition of soft athermal particles has long been explored by numerical models of undeformable spheres/circles and the researchers have extensively studied the critical behavior of the particles near jamming. It is now well known that the shear modulus of undeformable particles scales as the square root of the proximity to the jamming transition density. However, the square-root...
