JournalszaaVol. 18, No. 2pp. 247–266

Determining the Relaxation Kernel in Nonlinear One-Dimensional Viscoelasticity

  • Maurizio Grasselli

    Politecnico di Milano, Italy
Determining the Relaxation Kernel in Nonlinear One-Dimensional Viscoelasticity cover
Download PDF

Abstract

We consider a viscoelastic string whose mechanical behavior is governed by a non-linear stress-strain relationship. This constitutive law is characterized by a time-dependent relaxation kernel kk which is assumed to be unknown. The resulting motion equation is then associated with initial and Dirichlet boundary conditions. We show that the traction measurement at one end allows to identify kk. More precisely, we prove an existence and uniqueness result on a small time interval. Also, we show how the solution continuously depends on the data.

Cite this article

Maurizio Grasselli, Determining the Relaxation Kernel in Nonlinear One-Dimensional Viscoelasticity. Z. Anal. Anwend. 18 (1999), no. 2, pp. 247–266

DOI 10.4171/ZAA/880