各向同性Mullins效应非等温唯象模型的热力学框架
A thermodynamic framework for non-isothermal phenomenological models of isotropic Mullins effect
AI总结：
针对现有Mullins效应数学模型多局限于等温力学响应的问题，研究提出非等温唯象模型的热力学框架，明确相关储能与熵产机制，构建的热-力耦合模型符合热力学定律。
摘要：
Mullins效应是各类固体材料（尤其是填充橡胶）中一系列引人关注的非弹性响应的统称。鉴于Mullins效应的重要性，学界已开展诸多尝试以开发描述该效应的数学模型。然而，现有大多数模型仅聚焦于力学响应，且局限于理想化的等温环境。我们解除了对等温过程的限制，针对一类Mullins效应唯象模型提出了完整的热力学框架。具体而言，我们明确了储能机制（亥姆霍兹自由能）和熵产机制，二者在应力-应变关系层面可导致理想化Mullins效应或带永久应变的Mullins效应。在该框架下构建的模型可用于完全耦合的热-力学过程建模，且保证符合热力学定律。
英文摘要：
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.
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