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Materials (Basel). 2014 Jan 16;7(1):441-456. doi: 10.3390/ma7010441.

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

Author information

1
Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico. aelias@itesm.mx.
2
Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico. kl.baylon.phd.mty@itesm.mx.
3
Department of Mechanical Engineering and Industrial Construction, University of Girona, Maria Aurelia Capmany 61, Girona 17071, Spain. ines.iferrer@udg.edu.
4
Department of Mechanical Engineering and Industrial Construction, University of Girona, Maria Aurelia Capmany 61, Girona 17071, Spain. lidia.sereno@udg.edu.
5
Department of Mechanical Engineering and Industrial Construction, University of Girona, Maria Aurelia Capmany 61, Girona 17071, Spain. mluisa.gromeu@udg.edu.
6
Department of Mechanical Engineering and Industrial Construction, University of Girona, Maria Aurelia Capmany 61, Girona 17071, Spain. isabel.bagudanch@udg.edu.
7
Department of Mechanical Engineering and Industrial Construction, University of Girona, Maria Aurelia Capmany 61, Girona 17071, Spain. jordi.grabalosa@udg.edu.
8
Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico. tany.nohemi@gmail.com.
9
Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico. oscar.martinez@itesm.mx.
10
Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico. wlortega@gmail.com.
11
Centro de Investigación en Química Aplicada, Blvd. Enrique Reyna Hermosillo 140 Saltillo, Coahuila CP25250, Mexico. elizalde@ciqa.mx.

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:

biological tissues; biomaterial residual strains; pseudo-elasticity theory; rule of mixtures; stress-softening effects

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