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
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
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.