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Materials 2014, 7(1), 441-456; doi:10.3390/ma7010441
Article

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

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1 Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico 2 Department of Mechanical Engineering and Industrial Construction, University of Girona, Maria Aurelia Capmany 61, Girona 17071, Spain 3 Centro de Investigación en Química Aplicada, Blvd. Enrique Reyna Hermosillo 140 Saltillo, Coahuila CP25250, Mexico
* Author to whom correspondence should be addressed.
Received: 30 October 2013 / Revised: 23 December 2013 / Accepted: 7 January 2014 / Published: 16 January 2014
(This article belongs to the Section Biomaterials)
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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.
Keywords: stress-softening effects; biomaterial residual strains; biological tissues; rule of mixtures; pseudo-elasticity theory stress-softening effects; biomaterial residual strains; biological tissues; rule of mixtures; pseudo-elasticity theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Elías-Zúñiga, A.; Baylón, K.; Ferrer, I.; Serenó, L.; García-Romeu, M.L.; Bagudanch, I.; Grabalosa, J.; Pérez-Recio, T.; Martínez-Romero, O.; Ortega-Lara, W.; Elizalde, L.E. On the Rule of Mixtures for Predicting Stress-Softening and Residual Strain Effects in Biological Tissues and Biocompatible Materials. Materials 2014, 7, 441-456.

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