Static compression of a granular medium: The ''soft shell'' model

An assembly of spheroidal particles in Hertzian contact should display an elastic modulus <(mu)over bar> proportional to p(1/3) (where P is the pressure). We consider here a system where each particle (diameter d) is covered with a soft shell (thickness e, modulus mu) while the inside is rigid. This soft shell may, in practice, be an oxide layer. We then expect <(mu)over bar> similar to p(1/2) for a large range of pressures, in agreement with experiment. We also discuss the average conductance <(sigma)over bar>, assuming a small conductance in the soft shell, but ignoring tunnel effects. Then d similar to P-1/2.