Analysis and Implementation of Mixed-Mode Cohesive Zone Formulations for Cardiovascular Biomechanics Applications

Abstract

A comprehensive theoretical analysis of potential-based and non-potential-based cohesive zone models (CZMs) under mixed-mode conditions is presented. Using the well established Xu-Needleman (XN) CZM, it is demonstrated that unphysical repulsive normal tractions occur for potential-based CZMs under mixed-mode conditions when the mode II work of separation is greater than mode I work of separation. A modified form of the XN potential function (McGarry et al., 2012) is shown to significantly reduce the range of interface separations for which repulsive normal tractions occur. Normal-tangential coupling is then analysed for non-potential-based CZMs, demonstrating that correct penalisation of mixed-mode over-closure is not trivially achieved when a compression occurs at the interface. Two non-potential-based CZMs (McGarry et al., 2012) are shown to correctly penalise mixed-mode over-closure, in contrast to the non-potential CZM of van den Bosch et al. (2006). Finally, it is demonstrated that normal-tangential coupling must be based on the magnitude of interface separation in order to achieve fully mode-independent work of separation. CZMs are then used to simulate mixed-mode interface behaviour in three applied studies relating to the field of cardiovascular biomechanics: (i) In the first applied study, the traction distribution along a stent-coating interface is investigated in order to develop an enhanced understanding of the mechanisms of stent-coating debonding. Specifically, the influence of material and geometrical parameters on stent-coating interface tractions is analysed and conditions leading to mode I, mode II and mixed-mode coating delamination are uncovered; (ii) In the second applied study, interlayer dissection in an inhomogeneous abdominal aortic aneurysm (AAA) wall is simulated. Three patient-specific AAA geometries are reconstructed. Dissection is found to be primarily mode II in nature, accompanied by interface compression. The location and extent of interlayer dissection is found to be highly dependent on AAA geometry. Most importantly, predicted dissection locations are found to differ from locations of peak von Mises stress in the AAA wall; (iii) In the third applied study, mixed-mode debonding and rebonding of an endothelial cell from a silicone substrate is simulated. Cytoskeletal remodelling is found to be highly influenced by the form of the CZM used to describe the cell-substrate interface. The XN potential function leads to the computation of physically unrealistic repulsive normal tractions which prevent cell rebonding to the substrate. In contrast, such unphysical behaviour is not predicted when the modified potential function of McGarry et al. (2012) is used, and predicted cytoskeletal remodelling is found to correlate closely with published experimental data.