Constitutive equation describing the biaxial stress–strain behavior of poly(dimethylsiloxane) networks reinforced with silica generated in situ

The structure-based constitutive equation (its Langevin statistics-based connectivity term predicting the high-strain hardening, the tube-theory-based constraint term predicting the low-strain softening) proposed and tested by us for homogenous elastomeric networks has recently been extended for filler-reinforced networks by incorporating the concept of a strain-dependent strain-amplification factor (Polymer 1976). The equation was found to offer a very good description of stress–strain dependences in different deformation modes of pre-strain-softened filler-reinforced networks of natural and butadiene-styrene rubbers up to high-strains; the more complex high-strain behavior of virgin networks has also been described. The same equation is now shown to give a very good description and reasonable interpretation of published experimental data measured in different deformation modes (uniaxial extension, pure shear, equibiaxial extension) on poly(dimethylsiloxane) networks reinforced with silica precipitated in situ using the sol–gel process. The concentration dependence of the obtained parameter values is discussed.