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.
Highlights
Biological materials such as muscles, tendons, and skin are known to be very flexible and strong, and for this reason, these materials have attracted considerable interest with regard to the design of artificial materials or meta-materials [1,2]
It has been experimentally observed that the stress–strain diagram of soft biological materials is J-shaped and that the curve is composed of toe, heel, linear and rupture regions (Figure 1a,b) [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
These are the reasons for why we use the Finsler geometry (FG) modeling technique to analyze the experimental J-shaped diagrams. In addition to these features of FG modeling, it is important to note that the mechanical strength of real membranes, e.g., the surface tension represented by γ, becomes dependent on the position and direction on the surface [5,7]
Summary
Biological materials such as muscles, tendons, and skin are known to be very flexible and strong, and for this reason, these materials have attracted considerable interest with regard to the design of artificial materials or meta-materials [1,2]. The strains are used to obtain the diagram in those models, and the strains are calculated from the displacement field u, which is a part of the position variable r of polymers such that r = r0 + u This convention is useful if u is very small compared to r0 , and it is used in continuum mechanics or elasticity theory. To calculate the stress for example, we impose a constraint on the strain by fixing the polymer position r of the boundary This constraint induces an alignment of σ, and the induced internal structural change of σ causes a nontrivial behavior of mechanical property such as J-shaped diagram. In [33,34], we studied J-shaped curves by this FG modeling technique and obtained Monte Carlo (MC) data consistent with previously reported experimental results, in which the toe length is up to 40∼50% on the strain axis.
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