Shear bands as growing instabilities in viscoanelastic media with memory

Abstract

In this paper we  investigate the critical conditions under which a small perturbation in an homogeneous continuum can possibly grows into a shear band instability. In particular,  we analyze from a thermodynamical  viewpoint the phenomenon of shear bands in viscoanelastic media with memory. It is emphasized,  in the scientific literature, that the specific adopted rheology  strongly affects the results so that a special attention has to be paid, also for engineering purposes, to the accuracy of the  rheological model. Several well-known rheological model (for instance the so called Maxwell or Jeffreys media) are particular cases of the general model we  adopt in the paper to analyze shear bands. Instability conditions, giving  rise to shear bands formation, are obtained by introducing small perturbations around an homogeneous deformation into the system of differential equations governing the problem of homogeneous deformations in the considered continuous medium; as a result  a non-homogeneous linear dynamical system is obtained whose stability is analyzed. A research perspective in view of a possible  comparison with experimental results is proposed; in particular the simple methodology proposed in the paper should be applied in view of using the  phenomenon of the initiation of shear bands to calculate the thermomechanical coefficients of real materials.