Relaxed incremental variational approach for the modeling of damage-induced stress hysteresis in arterial walls
T. Schmidt, D. Balzani.
Journal of the Mechanical Behavior of Biomedical Materials, 58, 149-162, (2016)
In this paper, a three-dimensional relaxed incremental variational damage model is proposed, which enables the description of complex softening hysteresis as observed in supra-physiologically loaded arterial tissues, and which thereby avoids a loss of convexity of the underlying formulation. The proposed model extends the relaxed formulation of Balzani and Ortiz [2012. Relaxed incremental variational formulation for damage at large strains with application to fiber-reinforced materials and materials with truss-like microstructures. Int. J. Numer. Methods Eng. 92, 551-570], such that the typical stress-hysteresis observed in arterial tissues under cyclic loading can be described. This is mainly achieved by constructing a modified one-dimensional model accounting for cyclic loading in the individual fiber direction and numerically homogenizing the response taking into account a fiber orientation distribution function. A new solution strategy for the identification of the convexified stress potential is proposed based on an evolutionary algorithm which leads to an improved robustness compared to solely Newton-based optimization schemes. In order to enable an efficient adjustment of the new model to experimentally observed softening hysteresis, an adjustment scheme using a surrogate model is proposed. Therewith, the relaxed formulation is adjusted to experimental data in the supra-physiological domain of the media and adventitia of a human carotid artery. The performance of the model is then demonstrated in a finite element example of an overstretched artery. Although here three-dimensional thick-walled atherosclerotic arteries are considered, it is emphasized that the formulation can also directly be applied to thin-walled simulations of arteries using shell elements or other fiber-reinforced biomembranes. © 2015 Elsevier Ltd.
Keyword(s): mesh-independency, atherosclerotic arteries, soft biological tissues, softening, convexity, orientation distribution
Cite as: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84940759317&doi=10.1016%2fj.jmbbm.2015.08.005&partnerID=40&md5=c10b35ead3ebbabc944208d1cee1ca6c