Vol. 13, No. 1, 2018

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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.

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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