Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 18572, 12 pages

On internal constraints in continuum mechanics

K. R. Rajagopal1 and Giuseppe Saccomandi2

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.


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.