Percolation theory and physics of compression

Abstract

The concept of percolation theory is an excellent tool to elucidate the physics of compression. Earlier findings taking into account the percolation theory indicated that the formation of a tablet can be subdivided into a two-stage process with a ‘weak-bond’ percolation effect at a lower percolation threshold p c corresponding to the relative tapped density ϱ r and a ‘strong-bond/site’ percolation effect at an upper percolation threshold p c ∗ , i.e. at a relative density ϱ r ∗ , where brittle fracture and/or plastic flow starts to play an important role for the formation of a stable compact. The new findings which are now presented indicate that the uniaxial compression can be interpreted as a 2-dimensional percolation process where the stress is transmitted by the contact points of the particles. Thus the modified Young's elasticity modulus of the compact can be described by the fundamental equation of percolation theory with a critical exponent q = 1.3 (which is the conductivity exponent) and with a lower percolation threshold of the relative tapped density ϱ r. If the same equation is applied for the tensile strength, high values of the critical exponent result, indicating that a still unknown fractal dimension seems to play a key role.