Fatigue of self-healing hierarchical soft nanomaterials: The case study of the tendon in sportsmen
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Department of Physics and “Nanostructured Interfaces and Surfaces” Interdepartmental Centre, Università di Torino, Torino 10125, Italy
Matthew Merlino Department of Electrical Engineering & Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
Nicola M. Pugnoa) Laboratory of Bio-Inspired & Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, Università di Trento, Trento I-38123, Italy; Center for Materials and Microsystems, Fondazione Bruno Kessler, Povo (Trento) I-38123, Italy; and School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, United Kingdom (Received 7 July 2014; accepted 21 October 2014)
One of the defining properties of biological structural materials is self-healing, i.e., the ability to undergo long-term reparation after instantaneous damaging events, but also after microdamage due to repeated load cycling. To correctly model the fatigue life of such materials, self-healing must be included in fracture and fatigue laws, and related codes. Here, we adopt a numerical modelization of fatigue cycling of self-healing biological materials based on the hierarchical fiber bundle model and propose modifications in Griffith’s and Paris’ laws to account for the presence of self-healing. Simulations allow us to numerically verify these modified expressions and highlight the effect of the self-healing rate, in particular, for collagen-based materials such as human tendons and ligaments. The study highlights the effectiveness of the self healing process even for small healing rates and provides the possibility of improving the reliability of predictions of fatigue life in biomechanics, e.g., in sports medicine.
I. INTRODUCTION
Address all correspondence to this author. e-mail: [email protected] This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs. org/jmr-editor-manuscripts/. DOI: 10.1557/jmr.2014.335
modeling methods applied to such systems is given in Ref. 13. In biological materials, damage generally evolves as a consequence of cyclic loading during the whole lifetime of a particular tissue. Tendons and ligaments are typical examples. Their function is to transmit forces between bones and muscles or bones and other bones, and are constituted essentially by type I collagen fibers.1 As for other biological structural materials, they display a hierarchical structure that encompasses various size scales, ranging from collagen molecules (nanometer scale), to microfibrils, to fibrils, to fibers, to fiber fascicles, and to the final tissue itself (at cm scale).14 Thus, tendons and ligaments can be considered an example of “soft nanomaterials”. From a mechanical point of view, they can be modeled as bundles of viscoelastic fibers organized in a hierarchical structure, cyclically loaded in the fiber direction in uniaxial tension. Thus, a fiber bundle model-like app
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