  The Mullins effect is a common name for a family of intriguing inelastic
responses of various solid materials, in particular filled rubbers. Given the
importance of the Mullins effect, there have been many attempts to develop
mathematical models describing the effect. However, most of available models
focus exclusively on the mechanical response, and are restricted to the
idealised isothermal setting. We lift the restriction to isothermal processes,
and we propose a full thermodynamic framework for a class of phenomenological
models of the Mullins effect. In particular, we identify energy storage
mechanisms (Helmholtz free energy) and entropy production mechanisms that on
the level of stress--strain relation lead to the idealised Mullins effect or to
the Mullins effect with permanent strain. The models constructed within the
proposed framework can be used in the modelling of fully coupled
thermo-mechanical processes, and the models are guaranteed to be consistent
with the laws of thermodynamics.
