ON STEADY MOTIONS OF ISOTROPIC, ELASTIC COSSERAT POINTS

In this paper, a certain class of steady motions of compressible and i ncompressible isotropic, elastic Cosserat points are examined. We defi ne such a motion as a triad of deformed vectors undergoing a fixed axi s rotation at constant angular velocity. We strengthen and extend the results of Cohen, Lewis, Mac Sithigh, Muncaster and Simo, which employ the related theory of a pseudo-rigid body, by proving that the motion s they studied encompass the entire class of steady motions which we d efine. Several new results are established for the steady, motions of incompressible Cosserat points which include criteria for the existenc e of steady motions for all possible values of either an angular momen tum or an angular velocity. In the context of neo-Hookean and Mooney-R ivlin Cosserat points, we present and compare the results of two disti nct parametrizations (one based on angular velocity, the other based o n angular momentum) of the steady motions, and show that these motions are non-existent for a range of angular velocities. Furthermore, the qualitative similarity between the steady motions of certain compressi ble and incompressible Cosserat points is discussed. The results of th is paper can be interpreted in the context of the theory of a pseudo-r igid body.