The use of contravariant tensor invariants to model damage in anisotropic soft tissues

Abstract

Damage in soft biological tissues are a major domain of study as tissues may either undergo degradation with time or may experience in vivo failure during invasive procedures leading to a multitude of medical complications. Continuum damage models have been very successful recently to predict damage that can take place either due to fatigue loading, as a consequence of cyclic physiological loads or if the tissue is exposed to supra physiological loads especially during medical interventions. In this current work we use the mathematical framework of oblique contravariant tensors and their associated invariants to propose a damage function that takes into account the two important stages of progressive damage in collagen fibers (a) damage due to shear between matrix and fiber that can lead to debonding of the fibers and (b) total rupture of fibers. A model for the damage in the matrix has also been taken into account using the concept of equivalent stretch.The model was fitted with uniaxial experimental results from literature and showed very good agreement with the experimental data.

Keywords:

• Continuum damage
• contravariant tensors
• progressive damage