Density is pertinent as well as physical properties.
Stiff particles have the least stiffening effect, fibers have more and platelets have the most.
Voigt and Reuss laminates represent attainable bounds on the modulus of a composite.
Hierarchical coated sphere structures and hierarchical laminates allow one to attain Hashin-Shtrikman bounds bounds on the modulus of isotropic composites.
Bounds can be exceeded if the material does not obey one or more assumptions made in obtaining the bounds.
Properties can depend on direction.
The lower the symmetry, the more constants for physical properties.
New phenomena such as stretch-shear coupling can occur.
Some properties such as piezoelectricity and pyroelectricity require chiral asymmetry.
All materials exhibit thermal expansion and thermoelastic response.
Some coupled field properties such as piezoelectricity and pyroelectricity require chiral asymmetry.
Porous materials with interconnected void space exhibit coupling between deformation and fluid pressure and flow.
Practical composites contain fibers and laminations on different levels of scale.
Multiple size scales and functions occur in biological materials.
The largest structural elements, e. g. osteons, contribute to size effects and toughness.
High strength / weight can be obtained in hierarchical cellular solids.
Void space is a constituent that may be intentional or unintentional.
Cellular solids include honeycombs, foams, rib lattices and plate lattices.
Properties depend strongly on solid volume fraction.
The shape of the void space strongly affects properties.
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.
Nonclassical effects depend on the ratio of the material size scale to the experiment scale.
Time dependence and rate dependence.
Frequency dependence.
Dissipation of energy.
Vibration damping.
Attenuation of waves.
Viscoelasticity control via inclusion shape in composites.
Viscoelasticity caused by processes from interatomic scale to macroscopic coupled fields.
Unbounded viscoelastic damping in composites with a constrained unstable constituent.
Unbounded thermal expansion, piezoelectricity in two phase composites with void space or slip interfaces or with a constrained unstable constituent.
Stiffness greater than that of any constituent.