Thermal–electrical–chemical–mechanical coupling controls the behavior of many transport and electrochemical reactions processes in physical, chemical and biological systems. Hence, advanced understanding of the coupled behavior is crucial and attracting a large research interest. However, most of the existing coupling theories are limited to the partial coupling or particular process. In this paper, on the basis of irreversible thermodynamics, a variational principle for the thermal electrical chemical mechanical fully coupling problems is proposed. The complete fully coupling governing equations, including the heat conduction, mass diffusion, electrochemical reactions and electrostatic potential, are derived from the variational principle. Here, the piezoelectricity, conductivity, and electrochemical reactions are taken into account. Both the constitutive relations and evolving equations are fully coupled. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, piezoelectric and nonpiezoelectric dielectrics. As an application of this work, a developed boundary value problem is solved numerically in a mixed ion-electronic conductor (MIEC). Numerical results show that the coupling between electric field, diffusion, and chemical reactions influence the defect distribution, electrostatic potential and mechanical stress.
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November 2014
Research-Article
A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes
Pengfei Yu,
Pengfei Yu
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
e-mail: yupf9570@stu.xjtu.edu.cn
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University
,Xi'an 710049
, China
e-mail: yupf9570@stu.xjtu.edu.cn
Search for other works by this author on:
Shengping Shen
Shengping Shen
1
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
e-mail: sshen@mail.xjtu.edu.cn
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University
,Xi'an 710049
, China
e-mail: sshen@mail.xjtu.edu.cn
1Corresponding author.
Search for other works by this author on:
Pengfei Yu
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
e-mail: yupf9570@stu.xjtu.edu.cn
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University
,Xi'an 710049
, China
e-mail: yupf9570@stu.xjtu.edu.cn
Shengping Shen
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
e-mail: sshen@mail.xjtu.edu.cn
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University
,Xi'an 710049
, China
e-mail: sshen@mail.xjtu.edu.cn
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 20, 2014; final manuscript received September 8, 2014; accepted manuscript posted September 11, 2014; published online September 24, 2014. Editor: Yonggang Huang.
J. Appl. Mech. Nov 2014, 81(11): 111005 (12 pages)
Published Online: September 24, 2014
Article history
Received:
July 20, 2014
Revision Received:
September 8, 2014
Accepted:
September 11, 2014
Citation
Yu, P., and Shen, S. (September 24, 2014). "A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes." ASME. J. Appl. Mech. November 2014; 81(11): 111005. https://doi.org/10.1115/1.4028529
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