Undesirable Anisotropy in a Discrete Fiber Bundle Model of Fibrous Tissues

Abstract

Lanir (J Biomech. 16(1): [1][2][3][4][5][6][7][8][9][10][11][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.

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues

“…However, one limitation of this model, because of the discretization, is that the material response is not always isotropic even when the six weights are the same. To overcome this unphysical prediction, the authors improved the model by using a generalized strain invariant [30], and more recently by increasing the number of equally weighted fibre bundles [31] because the fitting of a large number of different weights is not practical.…”