Abstract
The problem of thermoviscoelastic quasi-static contact between a rod and a rigid obstacle, when the diffusion effect is taken into account, is modeled and analyzed. The contact is modeled by the Signorini's condition and the stress–strain constitutive equation is of the Kelvin–Voigt type. In the quasi-static case, the governing equations correspond to the coupling of an elliptic and two parabolic equations. It poses some new mathematical difficulties due to the nonlinear boundary conditions. The existence of solutions is proved as the limit of solutions to a penalized problem. Moreover, we show that the weak solution converges to zero exponentially as time goes to infinity. Finally, we give some computational results where the influence of diffusion and viscosity are illustrated in contact.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.