On the Rule of Mixtures for Predicting Stress-Softening and Residual Strain Effects in Biological Tissues and Biocompatible Materials

Abstract

In this work, we use the rule of mixtures to develop an equivalent material model in which the total strain energy density is split into the isotropic part related to the matrix component and the anisotropic energy contribution related to the fiber effects. For the isotropic energy part, we select the amended non-Gaussian strain energy density model, while the energy fiber effects are added by considering the equivalent anisotropic volumetric fraction contribution, as well as the isotropized representation form of the eight-chain energy model that accounts for the material anisotropic effects. Furthermore, our proposed material model uses a phenomenological non-monotonous softening function that predicts stress softening effects and has an energy term, derived from the pseudo-elasticity theory, that accounts for residual strain deformations. The model’s theoretical predictions are compared with experimental data collected from human vaginal tissues, mice skin, poly(glycolide-co-caprolactone) (PGC25 3-0) and polypropylene suture materials and tracheal and brain human tissues. In all cases examined here, our equivalent material model closely follows stress-softening and residual strain effects exhibited by experimental data.

Multiscale mechanics of macromolecular materials with unfolding domains

“…The first biological material we consider is the skin of mice whose experimental behavior reported in [35] is reproduced in Fig.8 a . A theoretical analysis in the pseudoelaticity framework of the hysteretic behavior of this biological tissue has been recently proposed in [52]. In the figure we represent by square dots the primary loading curve, by triangular dots the unloading curves, and by circular dots the reloading ones.…”

Effect of interface on the mechanical behavior of polybutadiene–silica composites: An experimental and simulation study

“…Improving the performance of polymer products by incorporating fillers has long been an important industrial activity, and traditionally this has been achieved by using materials such as carbon black, carbon nanofibers, clay, talc, and silica . Among them, the reinforcement of elastomers by silica has been studied in numerous studies .…”

Resolving the viscoelasticity and anisotropy dependence of the mechanical properties of skin from a porcine model

“…The rule of mixtures approach lends itself to many studies of the mechanical properties of soft connective tissues. In the context of skin, based on previous qualitative arguments that have applied the fibre composite principles for explaining the anisotropy of skin tissue (Lynch et al 2003), studies thereafter have extended the rule of mixtures approach for fibre composites (Piggott 2002) to predict (1) the total strain energy density of the skin, contributed by the respective tissue components associated with isotropy and anisotropy (Elias-Zuniga et al 2014) and (2) the second Piola-Kirchhoff stress tensor of skin, contributed by the stresses generated in the respective fibre and matrix components (Jor et al 2011)-weighted by the corresponding fractional composition of the components. With regards to stiffness, we argue that the tissue stiffness is directed by the stiffnesses of the fibre and matrix constituents.…”