Hydrostatic compression on polypropylene foam

Models currently used to simulate the impact behaviour of polymeric foam at high strain rates use data from mechanical tests. Uniaxial compression is the most common mechanical test used, but the results from this test alone are insufficient to characterise the foam response to three-dimensional stress states. A new experimental apparatus for the study of the foam behaviour under a state of hydrostatic stress is presented. A flywheel was modified to carry out compression tests at high strain rates, and a hydrostatic chamber designed to obtain the variation of stress with volumetric strain, as a function of density and deformation rate. High speed images of the sample deformation under pressure were analysed by image processing. Hydrostatic compression tests were carried out, on polypropylene foams, both quasi statically and at high strain rates. The stress–volumetric strain response of the foam was determined for samples of foam of density from 35 to 120 kg/m3, loaded at two strain rates. The foam response under hydrostatic compression shows a non-linear elastic stage, followed by a plastic plateau and densification. These were characterised by a compressibility modulus (the slope of the initial stage), a yield stress and a tangent modulus. The foam was transversely isotropic under hydrostatic compression

Attractor non-equilibrium stationary states in perturbed long-range interacting systems

Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself.Comment: 16 pages, 12 figure

Power law in the angular velocity distribution of a granular needle

We show how inelastic collisions induce a power law with exponent -3 in the decay of the angular velocity distribution of anisotropic particles with sufficiently small moment of inertia. We investigate this question within the Boltzmann kinetic theory for an elongated granular particle immersed in a bath. The power law persists so long as the collisions are inelastic for a large range of angular velocities provided the mass ratio of the anisotropic particle and the bath particles remains small. Suggestions for observing this peculiar feature are made.Comment: 8 pages, 4 figure

Kinetics of a frictional granular motor

Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained.Comment: 4 pages, 4 Figures, To be published in Phys. Rev. Let