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.

中文翻译：

---

Mullins 效应的非等温唯象模型的热力学框架

Mullins 效应是各种固体材料（尤其是填充橡胶）的一系列有趣的非弹性响应的通用名称。鉴于 Mullins 效应的重要性，已经有许多尝试开发描述该效应的数学模型。然而，大多数可用模型只关注机械响应，并且仅限于理想化的等温设置。我们解除了对等温过程的限制，并为一类穆林斯效应的现象学模型提出了一个完整的热力学框架。特别是，我们确定了能量存储机制（亥姆霍兹自由能）和熵产生机制，它们在应力-应变关系水平上导致理想化的穆林斯效应或永久应变的穆林斯效应。