ALEX 2018 Workshop: Abstracts

On the passage from nonlinear to linearized viscoelasticity

Martin Kružík

Institute of Information Theory and Automation, Czech Academy of Sciences (Czechia)

We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin‘s-Voigt‘s rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference. We identify weak solutions in the nonlinear framework as limits of time-incremental problems for vanishing time increment. Moreover, we show that linearization around the identity leads to the standard system for linearized viscoelasticity and that solutions of the nonlinear system converge in a suitable sense to solutions of the linear one. The same property holds for time-discrete approximations and we provide a corresponding commutativity result. This is a joint work with M. Friedrich (Münster).