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Research Papers

A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes

[+] Author and Article Information
Pengfei Yu

State Key Laboratory for Strength and
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,
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 81(11), 111005 (Sep 24, 2014) (12 pages) Paper No: JAM-14-1323; doi: 10.1115/1.4028529 History: Received July 20, 2014; Revised September 08, 2014; Accepted September 11, 2014

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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References

Figures

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Fig. 1

Configuration of the cross section of a planar electrolyte with all four edges fixed

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Fig. 2

Comparison among the present model with a = 0 and Swaminathan et al. [10]

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Fig. 3

Vacancy distribution for different applied voltages for (a) a = 5×10-12 and (b) a = 1×10-11

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Fig. 4

Vacancy distribution for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

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Fig. 5

Oxygen concentration for different applied voltages for (a) a = 0, (b) a = 5 × 10-12, and (c) a = 1 × 10-11

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Fig. 6

Oxygen concentration for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

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Fig. 7

Distribution of nondimensional electrostatic potentials for different applied voltages for (a) a = 0, (b) a = 5 × 10-12, and (c) a = 1 × 10-11

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Fig. 8

Distribution of nondimensional electrostatic potentials for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

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Fig. 9

Stress distribution for different applied voltages for (a) a = 0, (b) a = 5 × 10-12, and (c) a = 1 × 10-11

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Fig. 10

Stress distribution for different a for (a) V = 0, (b) V = 0.5, and (c) V = 1.01

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