Mapping forces in 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems

The effect of surface hardening on the elastic shakedown of elliptical contacts

The effect of varying both the aspect ratio and the coefficient of friction of contacts with elliptical geometry on their elastic shakedown performance has been examined theoretically for surfaces with two types of subsurface hardness or strength profiles. In stepwise hardening the hard layer is of uniform strength while in linear hardening its strength reduces from a maximum at the surface to that of the core at the base of the hardened layer. The shakedown load is expressed as the ratio of the maximum Hertzian pressure to the strength of the core material. As the depth of hardening, expressed as a multiple of the elliptical semi-axis, is increased so the potential shakedown load increases from a level that is appropriate to a uniform half-space of unhardened material to a value reflecting the hardness of the surface and near-surface material. In a step-hardened material, the shakedown limit for a surface 'pummelled' by the passage of a sequence of such loads reaches a cut-off or plateau value, which cannot be exceeded by further increases in hardening depth irrespective of the value of the friction coefficient. For a linear-hardened material the corresponding plateau is approached asymptotically. The work confirms earlier results on the upper bounds on shakedown of both point and line contacts and provides numerical values of shakedown loads for intermediate geometries. In general, the case depth required to achieve a given shakedown limit reduces in moving from a transversely moving nominal line load to an axisymmetric point load.

Effect of elastic stresses on free oscillations in ferroelectric liquid crystals

It is shown experimentally that an elastic mechanical stress in a crystal structure is a necessary factor for the appearance of free oscillations of the director of a ferroelectric liquid crystal. Such a mechanical stress arises as a result of internal textural perturbations in the presence of regions with a different orientation of the director or is produced by external pressure applied to one of the cell plates in the appropriate direction. © 1999 American Institute of Physics.

Isotropic constitutive models for metallic foams

The yield behaviour of two aluminum alloy foams (Alporas and Duocel) has been investigated for a range of axisymmetric compressive stress states. The initial yield surface has been measured, and the evolution of the yield surface has been explored for uniaxial and hydrostatic stress paths. It is found that the hydrostatic yield strength is of similar magnitude to the uniaxial yield strength. The yield surfaces are of quadratic shape in the stress space of mean stress versus effective stress, and evolve without corner formation. Two phenomenological isotropic constitutive models for the plastic behaviour are proposed. The first is based on a geometrically self-similar yield surface while the second is more complex and allows for a change in shape of the yield surface due to differential hardening along the hydrostatic and deviatoric axes. Good agreement is observed between the experimentally measured stress versus strain responses and the predictions of the models.