多孔介质的热-电-化-力学耦合理论及应用

THERMO-ELECTRO-CHEMO-MECHANICAL COUPLING THEORY AND ITS APPLICATION IN POROUS MEDIA

本文针对自然界中不同种类的多孔介质,评述了包含化学效应的多场耦合力学问题的国外内研究现状.介绍了研究多场耦合问题的理论架构,并基于Biot唯象理论和热力学理论,建立了一般性的热-电-化-力学多场耦合理论,在此基础上,以化学-力学耦合理论为特例,利用相应的控制方程和本构关系,给出了线性耦合系统的变分原理,并证明了化学-力学耦合理论架构的封闭性.基于所提出的化-力耦合模型,通过数值算例解释了多孔介质中的化学-力学耦合现象.最后对多孔介质,特别是对活体生物软组织中的多场耦合研究中存在的问题进行了讨论,并展望了本领域的未来发展趋势.

This paper presents an overview on the multi-field coupling model including chemical effects and its applications in various porous media which is widely distributed in nature. Basic theoretical frameworks of coupled multi-field problem are discussed in detail. Based on phenomenological Biot theory and thermodynamics, a general thermo-electro-chemo-mechanical coupling theory is presented and simplified version for chemo-mechanical coupled problem is then derived on that basis. Using the governing equations and constitutive laws of the theoretical model, a variational principle is deduced for a linearly coupled system and its closeness is proved. Several numerical examples are considered to illustrate the chemo-mechanical coupling phenomena of porous media and to verify the variational theory and numerical procedure presented. Finally, some problems and challenges in multi-field coupling problems in porous media especially in living biological soft tissue are analyzed, and future trends in this field are identified.