分野別セミナー

We develop a quasistatic nonlinear model for nonsimple viscoelastic materials ina finite-strain setting, based on
Kelvin-Voigt rheology. In this model, the viscos-ity stress tensor adheres to the principle of time-continuous frame-
indifference.Weak solutions in the nonlinear context are obtained as limits of time-incrementalproblems as the time
step approaches zero. Furthermore, we demonstrate thatlinearization around the identity results in the standard
system for linearized vis-coelasticity, and that solutions of the nonlinear system converge, in an appropri-ate sense,
to those of the linear system. This convergence property also appliesto time-discrete approximations, for which we
establish a commutativity result.This is based on joint work with M. Friedrich (Erlangen).