Modeling Dynamic Stress Softening as a Filler Network Effect

2 Modeling Dynamic Stress Softening as a Filler Network Effect 

It seem that percolation theory has his root in the works of Flory and Stockmayer who used it to study polymerization processes that may lead to gelation see D. Staufer, A. Aharony. Introduction to Percolation Theory. 2nd Ed., Taylor Francis, London, UK, 1994. ISBN 0 7484 0253 5. 

It is worth noting that dynamic strain softening is observed on filled vulcanizates whatever is the strain mode, i.e., shearing, tensile of uniaxial compression. The shear modulus G =G +iG is explicitly considered here, but the same considerations would in principle apply as well to the tensile modulus E =E +iE or the compliance / =/A/.  

To account for the strain-dependence of the dynamic moduli, Kraus considered that, at equilibrium the rates of aggregate deagglomeration and reagglomeration are equal and assumed that power law functions account for the strain dependency, i.e.  

Kraus model of deagglomeration-reagglomeration of filler aggregates, assimilated to soft spheres.  

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