No Cover Image

Journal article 145 views 16 downloads

The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

Arthesh Basak, Amirtham Rajagopal, Umesh Basappa, Mokarram Hossain Orcid Logo

International Journal of Applied Mechanics, Volume: 13, Issue: 3, Start page: 2150039

Swansea University Author: Mokarram Hossain Orcid Logo

Abstract

Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by...

Full description

Published in: International Journal of Applied Mechanics
ISSN: 1758-8251 1758-826X
Published: World Scientific Pub Co Pte Lt 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56784
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by the fibers. From histological studies on soft tissues it is evident that for a wide range of tissues the fibers have an oblique mean orientation about the physiological loading directions. Thus, we require a mathematical framework of tensors defined in nonorthogonal basis to capture the direction-dependent response of fibers under high induced loads. In this work, we propose a novel approach to determine the fiber strains with the aid of the contravariant tensors defined in an oblique coordinate system. To determine the fiber strains, we introduce a fourth-order contravariant fiber orientation transformation tensor. The approach helps us successfully in determining the fiber strains, for a family of symmetrically and asymmetrically oriented fibers, with the aid of a single anisotropic invariant. The proposed model was fitted with the experimental data from literature to determine the corresponding material parameters.
Keywords: Oblique coordinate system, reciprocal basis, anisotropic hyperelasticity
College: College of Engineering
Issue: 3
Start Page: 2150039