Fiber Dispersion-Dependent Failure in Biological Tissues: A Continuum Mechanics Approach

Accurate failure prediction methods are crucial in the evaluation of biological tissues prone to failure. These methods have been extensively studied in isotropic modes, but remain underexplored in fiber dispersion of biological tissues with varying anisotropic dispersion effects. The present work aims to investigate the often-overlooked role of fiber dispersion in improving the prediction of uniaxial and biaxial failure stresses of biological tissues. The strain energy density is formulated as a function of fiber dispersion using a well-established generalized structural tensor framework. The influence of fiber orientations and fiber dispersion on failure behavior is illustrated for anisotropic tissues by comparing anisotropic modes, with and without fiber dispersion effects to isotropic modes. Variations in failure envelopes are also analyzed for different fiber orientations and degrees of nonlinearity in the dispersion terms across uniaxial and non-equibiaxial deformation. Furthermore, the effect of fiber dispersion on stress-stretch behavior is illustrated using experimental data from human lower urinary tract tissues, including the bladder, prostate, buck’s fascia, and tunica albuginea, as well as tissue samples from the lower thoracic region of a pig, through comparisons between anisotropic and isotropic models with and without fiber dispersion effects.