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Multi-scale modelling of rubber-like materials and soft tissues: an appraisal - PubMed

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Multi-scale modelling of rubber-like materials and soft tissues: an appraisal

G Puglisi et al. Proc Math Phys Eng Sci. 2016 Mar.

Abstract

We survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro- and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties.

Keywords: entropic elasticity; multi-scale models; rubber elasticity.

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Figures

Figure 1.
Figure 1.

A cartoon of the ‘FJC tube model’ is obtained from this picture if we consider a straight tube. Then the projection of the rods composing the macromolecule on the axis of the cylinder is easy to obtain. On the other hand, if we consider a curved tube, as is clearly the case in an entangled network, then the same projection depends on the curvature of the axis of the tube. In such a way, we introduce additional parameters (the persistence length) and we obtain a different model [59].

Figure 2.
Figure 2.

A cartoon of the basic model we propose where the network is composed of entropic non-Gaussian chains and linear elastic springs.

Figure 3.
Figure 3.

In the curves in (a,c), we have an ideal material composed by a mixture where the hard phase has a principal role. In (b,d), we have an ideal material where the soft phase plays the main role.

Figure 4.
Figure 4.

The sub-plot (a) shows a cartoon of the macromolecule composed by rods and bubbles, i.e. structures that contain a reservoir of monomers and if opened change the contour length of the molecule. In (b), we plot the total energy (Griffith-like) minimization method. Opening of a bubble has a twofold effect: it dissipates a certain amount of energy Q and it increases the contour length thus changing the elastic curve. Despite this complexity, the minimization of the overall energy is possible. The corresponding sawtooth force [69] end-to-end length diagram is represented in (c), reproducing the AFM experimental behaviour of the single macromolecule in [24]. In (d) and (e), based on an 8-chain cell scheme, we reproduce [70] the cyclic loading for mouse skin studied in [71] and the shear cycles of pig (passive) myocardium tissues reported in [72], respectively. In (f), based on a 3-chain scheme, we reproduce the experimental behaviour of Senegalensis Nephila spider silks from [73].

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