Lanir (J Biomech. 16(1):1–12, 1983) proposed a structural model for the anisotropic response of fibrous tissues with fiber bundles oriented in space by a continuous orientation distribution. Each fiber bundle was assumed to have the same undulation distribution that characterizes its nonlinear elastic response. Recently, a
discrete fiber icosahedron model for fibrous soft tissues has been introduced, which is based on fiber bundles parallel to the six lines that connect opposing vertices
of a regular icosahedron. Although the parameters in the icosahedron model can be determined to match experimental data for the anisotropic response of various tissues, the icosahedron model predicts anisotropic response when the weights of the six fiber bundles are equal. This chapter quantifies this undesirable anisotropic response and refers to a new icosahedron model based on a generalized invariant which also matches experimental data and analytically reduces to an isotropic form when the weights of the fiber bundles are equal.