In 1964, Green and Rivlin [1, 2] proposed two non-standard theories of continua. Both papers concerned non-simple materials: the first considered deformation gradients of higher order than the first as dependent variables; and the second, which generalised the first, treated materials whose kinematic state was not completely detemined by the deformation function, but was also dependent upon some multipolar deformation functions. In both theories the existence of higher order stresses is fundamental.
In this paper we present some preliminary results for stability and instability in these theories in the special but important case of elastic materials.
@article{urn:eudml:doc:38820,
title = {On the stability of multipolar elastic materials.},
journal = {Stochastica},
volume = {3},
year = {1979},
pages = {79-95},
zbl = {0434.73002},
mrnumber = {MR0556649},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38820}
}
Wilkes, N. S. On the stability of multipolar elastic materials.. Stochastica, Tome 3 (1979) pp. 79-95. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38820/