期刊
JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS
卷 58, 期 -, 页码 149-162出版社
ELSEVIER
DOI: 10.1016/j.jmbbm.2015.08.005
关键词
Mesh-independency; Atherosclerotic arteries; Soft biological tissues; Softening; Convexity; Orientation distribution
资金
- German Science Foundation (DFG) [BA 2823/5-3]
- DFG in the context of the institutional strategy The Synergetic University at TU Dresden
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. (C) 2015 Elsevier Ltd. All rights reserved.
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