Constitutive Relations for the Thermoviscoelasticity of Diphase Medium with a Kelvin-Voigt Rheological Skeleton

World Multidisciplinary Earth Sciences Symposium

Bartlewska-Urban, Monika^1 ; Strzelecki, Tomasz^2

Wroclaw University of Science and Technology, Faculty of Geoengineering Mining and Geology, 15 Na Grobli st., Wroclaw

50-421, Poland^1

Wroclaw University of Science and Technology, Faculty of Technology and Natural Sciences, 9 S. Batory st., Legnica

59-200, Poland^2

关键词: Biot consolidation theory;    Constitutive relations;    Heat conduction equations;    Irreversible thermodynamics;    Representative elementary volume;    Second Law of Thermodynamics;    Thermal consolidation;    Thermoviscoelasticity;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/221/1/012015/pdf
DOI  :  10.1088/1755-1315/221/1/012015

来源: IOP

【 摘 要 】

Constitutive relations for a diphase medium consisting of a viscoelastic Kelvin-Voigt skeleton and a compressible Newtonian liquid filling the pores of the medium were derived from the equations of irreversible thermodynamics, assuming the thermoviscoelasticity process to be non-isothermal. The rate of change in internal energy in the two phases of the diphase medium was determined from the first law of irreversible thermodynamics. Physical relations for the solid phase and the liquid filling the pores of the medium, and an equation of entropy were determined using Helmholtz free energy and the second law of thermodynamics for open systems. The temperature of the medium's two phases in the heat conduction process was assumed to be identical for the representative elementary volume (RVE). Stresses, related to the total sur-face of RVE, for the diphase medium solid phase and liquid phase, were defined according to the Darcy-Biot consolidation theory. The derived constitutive relations and the heat conduction equation are linear since the expansion of the function of Helmholz free energy into a Taylor series was limited to the second order. In reality, however, as the temperature increases, the model becomes nonlinear. Therefore, the applicability of the proposed model is limited to certain intervals of change in the temperature of the solid body and the liquid. The constitutive relations for the elastic skeleton come down to relations for the thermal consolidation of the Biot-Darcy body.