| Abstract: |
| We consider a Kelvin-Voigt model for thermoviscoelastic second-grade materials, where the elastic and the viscous stress tensor both satisfy frame indifference. We prove the existence of weak solutions relying on an estimate due to Ciarlet and Mardare (2015), which generalizes the celebrated rigidity estimate of Friesecke, James, and M\uller (2002). The estimate allows us to employ a staggered time-discretization scheme that preserves frame indifference, in which the deformation and the temperature are updated alternately.
The talk is based on joint works with Manuel Friedrich, Martin Kru\v{z}\`ik, Rufat Badal, and Martin Hor\`{a}k. |
|