Article,
A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber
International Journal of Solids and Structures, 41 (7): 1855--1878 (April 2004)
Abstract
Stress softening during initial loading cycles, known as the Mullins
effect, and the residual strain upon unloading are not accounted
for when the mechanical properties of rubber are represented in terms
of a strain-energy function, i.e. if the material is modelled as
hyperelastic. In this paper we first describe some experimental results
that illustrate stress softening in particle-reinforced rubber together
with associated residual strain effects. In particular, the results
show how the stress softening and residual strain change with the
magnitude of the applied strain. Then, on the basis of these data
a constitutive model is derived to describe this behaviour. The theory
of pseudo-elasticity is used for this model, the basis of which is
the inclusion of two variables in the energy function in order separately
to capture the stress softening and residual strain effects. The
dissipation of energy, i.e. the difference between the energy input
during loading and the energy returned on unloading is also accounted
for in the model by the use of a dissipation function, which evolves
with the deformation history.
