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.
