Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials
Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials
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DOI：
10.3390/polym10070715
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发表时间：
2018-06
期刊：
影响因子：
5
通讯作者：
Kazuhiko Mitsuhashi;S. Ghosh;H. Koibuchi
中科院分区：
文献类型：
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作者：
Kazuhiko Mitsuhashi;S. Ghosh;H. Koibuchi
在此，我们研究的应力-应变图的软生物材料，如动物的皮肤，肌肉和动脉Finsler几何（FG）建模。这些生物材料的应力-应变图总是J形的，由趾部、跟部、线性和失效区域组成。在趾部区域中，应力几乎为零，并且该零应力区域的长度在例如某些动脉中变得非常大（约150%）。在本文中，我们研究长趾图使用二维（2D）和3D FG建模技术和蒙特卡罗（MC）模拟。我们发现，除了破坏区域，大应变J形图成功地再现FG模型。这意味着复杂的J形曲线源自聚合物分子的方向和位置自由度之间的相互作用，如FG模型中所实现的。
Herein, we study stress–strain diagrams of soft biological materials such as animal skin, muscles, and arteries by Finsler geometry (FG) modeling. The stress–strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear, and failure regions. In the toe region, the stress is almost zero, and the length of this zero-stress region becomes very large (≃150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that, except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.