Mesoscopic bead-and-spring model of hard spherical particles in a rubber matrix. I. Hydrodynamic reinforcement

Exploiting an electrostatic analogy, we show that the elastic forces betwee n a set of rigid particles embedded in a phantom polymer network can be rep resented by a simple bead-and-spring model. The beads represent the particl es and the springs the rubber matrix. The model is validated by Monte Carlo simulation of rubbers filled with hard spherical particles, at volume frac tions between 0.1 and 0.3. We derive both the moduli and the full stress-st rain curves, under uniaxial elongation. The model reproduces and extends pr evious theoretical results on the so-called hydrodynamic reinforcement effe ct. (C) 2000 American Institute of Physics. [S0021-9606(00)70141-3].