Freedom in solid materials

Freedom in elasticity: spatial
Uniconstant elasticity: Poisson's ratio ν = 1/4 for all materials
Classical elasticity: ν between -1 and 0.5 (isotropic). ν ~ 1/3 for most materials. Attainment of any Poisson's ratio in that range.
Cosserat elasticity: Rotational freedom of points; enhanced toughness.

Structural hierarchy.
Multiple functions in biological materials
Role of the largest structural elements, e. g. osteons
High strength / weight in cellular solids

Viscoelasticity: energy dissipation, time dependence and frequency dependence.

Nonlinearity: strain dependence and stress dependence.

Materials with extreme properties
Materials inspired by structures in living systems

Unbounded damping

Unbounded thermal expansion, piezoelectricity

Stiffness greater than that of any constituent











Bone exhibits size effects in rigidity.
Strain gradients on the scale of the cortex thickness give rise to large effects.
















Viscoelastic damping in bone exhibits a minimum at frequencies associated with normal activities. Pressure due to fluid in Haversian systems is at ultrasonic frequencies.
















Nonlinear viscoelasticity in ligament exhibits rate (power in time) which depends on stress in creep and upon strain in relaxation.
Relaxation occurs faster than creep.
This behavior is not describable by quasilinear viscoelasticity (QLV) but is describable by nonlinear superposition.