Biomechanics of Arterial Walls under Supra-Physiological Loading Conditions

点击翻译按钮获取中文摘要

In this research project supra-physiological loading situations of arterial walls, e.g., occurring during balloon angioplasty, are described. Under such loading conditions microscopic damage on the interfibrillar level is induced in the tissue leading to a complex softening hysteresis observed in the stress-strain response. To describe this behavior, damage models were developed in the first phase of this project on the basis of continuum damage mechanics. These models were compared with experiments and a good correlation could be shown. However, the loss of ellipticity, which is typically observed for damage mechanics formulations, may lead to mesh-dependent solutions and the loss of material stability. In order to solve these substantial fundamental problems, mathematically secured and robust modeling approaches are central task in this second phase. The basis is the construction of an incremental variational formulation for damage in soft biological tissues which enables convexification. Thereby, the loss of ellipticity can be precluded and mesh-independent solutions as well as material stability are ensured. Essentially, efficient models and algorithms are planned to be developed on the basis of relaxed incremental variational formulations, which reflect the specific characteristics of the damage hysteresis in soft biological tissues. Starting from a rather phenomenological but efficient approach which is to be constructed first, a model has to be developed, which takes into account fiber dispersion. Thereby damage evolution is described by a progressive recruitment of individual fiber orientations. In order to enable an optimized parameter adjustment in the sense of a least-square minimization in reasonable time also for this model, a surrogate model is planned to be constructed and used during parameter optimization. The developed formulations have to be implemented in a finite-element program. Then they have to be analyzed with respect to their performance on the basis of boundary value problems where diseased arterial walls are simulated.