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Polymers 2018, 10(7), 715; https://doi.org/10.3390/polym10070715

Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials

Department of Industrial Engineering, National Institute of Technology, Ibaraki College, Nakane 866, Hitachinaka, Ibaraki 312-8508, Japan
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Received: 28 May 2018 / Revised: 25 June 2018 / Accepted: 27 June 2018 / Published: 29 June 2018
(This article belongs to the Special Issue Mechanical Behavior of Polymers)
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Abstract

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. View Full-Text
Keywords: soft biological materials; stress–strain diagram; J-shaped diagram; Monte Carlo; statistical mechanics; Finsler geometry soft biological materials; stress–strain diagram; J-shaped diagram; Monte Carlo; statistical mechanics; Finsler geometry
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Mitsuhashi, K.; Ghosh, S.; Koibuchi, H. Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials. Polymers 2018, 10, 715.

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