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).