An invited lecture in the Department of Mechanical & Materials Engineering
On the inverse Noeter’s theorem in nonlinear micropolar continua
Professor Jovo Jaric
Faculty of Mathematics, University of Belgrade
Studentski trg 16, Belgrade, Serbia & Montenegro
In a paper by Knowles & Steinberg it was shown that the conservation law
J (G)  e   (W n  x T T) dS
G
(where G denotes any smooth non-self intersecting closed surface “path of integration surrounding the
crack”, n is the unit outward normal vector on G, e is unit vector in the direction of the crack propagation,
T is stress tensor, W is the strain-energy density at the point x, x  Grad x ), follows from an
application of Noether’s theorem [2] on invariant variational principles to the principle of minimum
potential energy in elastostatics. Roughly speaking, Noether’s theorem states that if a given set of
differential equations can be identified as the Euler-Lagrange equations corresponding to a variational
principle which remains invariant under an n-parameter group of infinitesimal transformations, then there
exists an associated set of n conservation laws satisfied by all solutions of the original differential
equations. This presentation is structured as follows: first the notation to be used in the remainder and
mathematical preliminaries is introduced. Then, the version of Noether’s theorem appropriate for present
purposes is stated. Next, we present a brief review of nonlinear micropolar continuum. This is followed
by the principal results of inverse Noether’s theorem we discussed. The proof of the theorem is original
and very simple. This theorem provides us with the generators of group of infinitesimal transformations.
Then the completeness of conservation laws is established.
1. Knowles & Steinberg, On a class of conservation laws in linearized and finite elasticity, Archive
of Rational Mechanics and Analysis, 44, 187 (1972).
Date:
Time:
Room:
October 23, 2003 (THURSDAY)
2:20 p.m. - 3:10 p.m.
EC 2300
Brief Vitae of the Invited Speaker:
Secretary General of Yugoslav Society of Mechanics, Dean of the Faculty of Mathematics and Natural Sciences,
The University of Belgrade, member of New York Academy of Sciences. His research is in the basic problems of
continuum mechanics: Constitutive equations, Theory of elasticity, Conservation laws, Noether’s theorem applied in
continuum mechanics, J- integral and configurational forces, wave propagation-singular surfaces, Mathematical
methods in continuum mechanics, Tensor calculus applied to differential geometry and mechanics, group theory. He
is author (coauthor) of more then 60 journals papers and author of two books.
For further information please contact Prof. G. S. Dulikravich at 305-348-7016 or at dulikrav@fiu.edu.