By incorporating two different fracture mechanisms and salient unilateral effects in rock materials,we propose a thermomechanical phase-field model to capture thermally induced fracture and shear heating in the proces...By incorporating two different fracture mechanisms and salient unilateral effects in rock materials,we propose a thermomechanical phase-field model to capture thermally induced fracture and shear heating in the process of rock failure.The heat conduction equation is derived,from which the plastic dissipation is treated as a heat source.We then ascertain the effect of the non-associated plastic flow on frictional dissipation and show how it improves the predictive capability of the proposed model.Taking advantage of the multiscale analysis,we propose a phase-field-dependent thermal conductivity with considering the unilateral effect of fracture.After proposing a robust algorithm for solving involved three-field coupling and damage-plasticity coupling problems,we present three numerical examples to illustrate the abilities of our proposed model in capturing various thermo-mechanically coupled behaviors.展开更多
The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a c...The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.展开更多
基金funding provided by the National Natural Science Foundation of China(No.12202137)TY's contribution is funded by the China and Germany Postdoctoral Exchange Program(Grant No.ZD202137).The first author(TY)would like to express his gratitude to Prof.Keita Yoshioka for reviewing this manuscript and for his invaluable feedback.
文摘By incorporating two different fracture mechanisms and salient unilateral effects in rock materials,we propose a thermomechanical phase-field model to capture thermally induced fracture and shear heating in the process of rock failure.The heat conduction equation is derived,from which the plastic dissipation is treated as a heat source.We then ascertain the effect of the non-associated plastic flow on frictional dissipation and show how it improves the predictive capability of the proposed model.Taking advantage of the multiscale analysis,we propose a phase-field-dependent thermal conductivity with considering the unilateral effect of fracture.After proposing a robust algorithm for solving involved three-field coupling and damage-plasticity coupling problems,we present three numerical examples to illustrate the abilities of our proposed model in capturing various thermo-mechanically coupled behaviors.
文摘The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.
