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bioRxiv · 10.1101/275206

Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues

Koibuchi, H.·Mitsuhashi, K.·Ghosh, S.
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Abstract

Herein, we study stress-strain diagrams of soft biological tissues 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 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.

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Koibuchi, H., Mitsuhashi, K., Ghosh, S.. 2018-03-08. Mathematical modeling and simulations for large-strain J-shaped diagrams of soft biological tissues. https://doi.org/10.1101/275206

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