One-dimensional motion of a material with a strain theshold

  • A. Farina Università degli Studi di Firenze
  • A. Fasano Università degli Studi di Firenze
  • L. Fusi Università degli Studi di Firenze
  • K.R. Rajagopal Texas A&M University
Keywords: Implicit constitutive theories, Free boundary problems, Wave equation

Abstract

We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity) are continuous across the propagating interface for the strain threshold .
Local existence and uniqueness are proved for the continuous case (in which the interface propagation is subsonic). Some explicit solutions are calculated for another case (with a supersonic interface). It is shown that the model with strain threshold is never the limit of hyperelastic systems.

Author Biographies

A. Farina, Università degli Studi di Firenze
Dipartimento di Matematica “U. Dini”,
Viale Morgagni 67/a, 50134 Firenze, Italy
A. Fasano, Università degli Studi di Firenze
Dipartimento di Matematica “U. Dini”,
Viale Morgagni 67/a, 50134 Firenze, Italy
L. Fusi, Università degli Studi di Firenze
Dipartimento di Matematica “U. Dini”,
Viale Morgagni 67/a, 50134 Firenze, Italy
K.R. Rajagopal, Texas A&M University
Department of Mechanical Engineering
College Station, Texas 77843, USA
Published
2007-12-06
Section
Articoli