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On the passage from nonlinear to linearized viscoelasticity

Presented by: 
Martin Kruzik Academy of Sciences of the Czech Republic, Czech Technical University
Date: 
Wednesday 13th February 2019 - 16:00 to 16:40
Venue: 
INI Seminar Room 2
Abstract: 
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a nite-strain setting in the Kelvin`s-Voigt`s rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indierence. 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 (Munster).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons