Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 18572, 12 pages
doi:10.1155/DENM/2006/18572
On internal constraints in continuum mechanics
1Department of Mechanical Engineering, Texas A & M University, College Station, TX 77845, USA
2Dipartimento di Ingegneria dell'Innovazione, Università degli Studi di Lecce, Lecce 73100, Italy
Received 18 June 2005; Accepted 22 August 2005
Dedicated to Professor Piero Villaggio on the occasion of his seventieth birthday
Copyright © 2006 K. R. Rajagopal and Giuseppe Saccomandi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In classical particle mechanics, it is well understood that while
working with nonholonomic and nonideal constraints, one cannot
expect that the constraint be workless. It is curious that in
continuum mechanics, however, the implications of the result in
classical mechanics have not been clearly understood. In this paper,
we show that in dealing with the response of dissipative systems,
one cannot require that constraints do no work or ignore the fact
that the material response functions depend on the constraint
reaction. An example of this is the viscosity of a fluid depending
on the pressure.