A micromechanical model to predict damage and failure in biological tissues. Application to the ligament-to-bone attachment in the human knee joint

Abstract 

Computational models are developed in injury biomechanics to assess lesions in biological tissues based on mechanical measurements. The linear mechanics of fracture theory (LMFT) is a common approach to establish injuries based on thresholds (such as force or strain thresholds) which are straightforward to implement and computationally efficient. However, LMFT does not apply to non-linear heterogeneous materials and does not have the ability to predict failure onset. This paper proposes the cohesive zone model theory (CZMT) as an alternative. CZMT focuses on the development of behaviour laws for crack initiation and propagation at an interface that apply within a fibrous material or at the interface between materials. With the view of evaluating CZMT for biological tissues, the model developed by Raous et al. [1999. A consistent model coupling adhesion, friction and unilateral contact. Comput. Methods Appl. Mech. Eng., 177, 383–399] was applied to the ligament-to-bone interface in the human knee joint. This model accounts for adhesion, friction and damage at the interface and provides a smooth transition from total adhesion to complete failure through the intensity of adhesion variable. A 2D finite element model was developed to mimic previous experiments, and the model parameters were determined using a dichotomy method. The model showed good results by its ability to predict damage. The extension to a 3D geometry, with an inverse problem approach, is, however, required to better estimate the model parameters values. Although it is computationally costly, CZMT supplements the improvements achieved in microimaging techniques to support the development of micro/macro approaches in biomechanical modelling.

Keywords: Adhesion, Cohesive zone model, Failure, Micromechanics, Ligament-to-bone attachment, Damage