Stability of Cosserat solids: size effects, ellipticity and waves

Lakes, Roderic S.

doi:10.2140/jomms.2018.13.83

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Stability of Cosserat solids: size effects, ellipticity and waves

Roderic S. Lakes

Vol. 13 (2018), No. 1, 83–91

DOI: 10.2140/jomms.2018.13.83

Abstract

We consider stability in Cosserat solids. To obtain restrictions on elastic constants based on positive definite strain energy, energy terms are tacitly assumed to be independent. In finite-size objects, however, the terms are linked in Cosserat materials. Therefore, in contrast to classical solids, the stability of Cosserat solids appears to depend on the size and shape of the specimen, provided strong ellipticity is satisfied. Stability in the presence of stored energy is possible. Solids with microstructure and stored energy offer the potential to facilitate attainment of extreme behavior in the presence of spatial gradients. Snap-through buckling in torsion is envisaged by analogy to the axial buckling concept used for composites with negative stiffness inclusions. It is possible to support compressive load in a stable manner but to dissipate energy in the presence of spatial gradients as in torsion or bending.

Keywords

Cosserat, stability, micropolar

Milestones

Received: 14 September 2017

Revised: 7 November 2017

Accepted: 14 November 2017

Published: 7 April 2018

Authors

Roderic S. Lakes
Department of Engineering Physics University of Wisconsin-Madison Madison, WI United States

Vol. 13, No. 1, 2018

Roderic S. Lakes

Abstract

Keywords

Milestones

Authors