Uniconstant elasticity: Poisson's ratio ν = 1/4 for all materials. Based on a model of interatomic force: central forces, affine deformation.
Classical elasticity: ν between -1 and 0.5 (isotropic) via tensors and continuum concept.
ν ~ 1/3 for most materials.
Attainment of any Poisson's ratio in that range.
No length scale in classical elasticity.
Chirality has no effect in classical elasticity.
Wave speed independent of frequency in classical elasticity.
Cosserat elasticity: Rotational freedom of points.
There is a length scale in the theory.
Size effects in rigidity are observed in bone, foams and lattices.
Strain gradients on the scale of the specimen thickness give rise to large effects.
Chiral structure gives rise to coupling between stretch or squeeze and twist.
Wave speed depends on frequency.
Piezoelectric response can be sensitive to strain gradient, recently called flexo-electricity.
Length scale effects depend on the ratio of the material length scale to length scales in the experiment, not on the absolute length scale.