The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

Biological tissues have been shown to behave isotropically at lower strain values, while higher strains the fibers embedded in tissue straighten and tend take up load. Thus, anisotropy induced loads can be mathematically modeled by incorporating experienced fibers. From histological studies on soft it is evident that for a wide range of an oblique mean orientation about physiological loading directions. we require mathematical framework tensors defined nonorthogonal basis capture direction-dependent response under high loads. In this work, propose novel approach determine fiber with aid contravariant coordinate system. To strains, introduce fourth-order transformation tensor. The helps us successfully determining family symmetrically asymmetrically oriented fibers, single anisotropic invariant. proposed model was fitted experimental data from literature corresponding material parameters.