  Constitutive equations are derived for the time-dependent behavior of
particle-reinforced elastomers at isothermal loading with finite strains. A
rubbery polymer is modelled as a network of macromolecules bridged by junctions
which can slip with respect to the bulk material under straining. A filled
elastomer is thought of as an ensemble of meso-regions where sliding occurs
with different rates. Stress-strain relations for a particle-reinforced rubber
are developed by using the laws of thermodynamics. For tensile relaxation
tests, these equations are characterized by three adjustable parameters. To
determine the experimental constants, three series of relaxation tests are
performed for longitudinal strains in the range from 100 to 250 %. By fitting
observations, the influence of pre-loading and thermal recovery is analyzed on
the nonlinear viscoelastic response of natural rubber reinforced with carbon
black.
