  Hyperelastic models have been widely used to model polymers and soft tissues.
However, most hyperelastic models are phenomenological material models. Based
on statistical mechanics and molecular chain configuration, 8 chain model or
Arruda-Boyce model is a physical model which can be used to understand how
microstructures of chains affect macroscopic mechanical properties of polymers
and soft tissues. Mechanical properties of many polymers and soft tissues are
directional dependent. Polymer matrix can be reinforced by fibers. For soft
tissues, ligaments and tendons will lead to anisotropic properties. Since
matrix and reinforcements are composed of similar microstructural molecular
chains, they can be modeled by using the same mathematical model. In this
paper, a series of 8 chain models is used to understand composite properties.
That is, an isotropic 8 chain model will be used to model matrix and
anisotropic 8 chain models will be used to model fibers. Replacing I_1 in
isotropic 8 chain model with I_4 in anisotropic 8 chain model is physically
corresponding to changing representative 8 chain cubic cell to 8 chain slender
cell. This treatment not only simplifies exist anisotropic mathematical
structures but also keeps microscopic physics of 8 chain model unchanged.
