Finite strain response of crimped fibers under uniaxial traction

An analytical approach applied to collagen

authored by: Michele Marino, Peter Wriggers
Abstract: Composite materials reinforced by crimped fibers intervene in a number of advanced structural applications. Accordingly, constitutive equations describing their anisotropic behavior and explicitly accounting for fiber properties are needed for modeling and design purposes. To this aim, the finite strain response of crimped beams under uniaxial traction is herein addressed by obtaining analytical relationships based on the Principle of Virtual Works. The model is applied to collagen fibers in soft biological tissues, coupling geometric nonlinearities related to fiber crimp with material nonlinearities due to nanoscale mechanisms. Several numerical applications are presented, addressing the influence of geometric and material features. Available experimental data for tendons are reproduced, integrating the proposed approach within an optimization procedure for data fitting. The obtained results highlight the effectiveness of the proposed approach in correlating fibers structure with composite material mechanics.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Journal of the Mechanics and Physics of Solids
Volume: 98
Pages: 429-453
No. of pages: 25
ISSN: 0022-5096
Publication date: 09.06.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.jmps.2016.05.010 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{88012c8f1b22458ab74d527a160a0551,
title = "Finite strain response of crimped fibers under uniaxial traction: An analytical approach applied to collagen",
abstract = "Composite materials reinforced by crimped fibers intervene in a number of advanced structural applications. Accordingly, constitutive equations describing their anisotropic behavior and explicitly accounting for fiber properties are needed for modeling and design purposes. To this aim, the finite strain response of crimped beams under uniaxial traction is herein addressed by obtaining analytical relationships based on the Principle of Virtual Works. The model is applied to collagen fibers in soft biological tissues, coupling geometric nonlinearities related to fiber crimp with material nonlinearities due to nanoscale mechanisms. Several numerical applications are presented, addressing the influence of geometric and material features. Available experimental data for tendons are reproduced, integrating the proposed approach within an optimization procedure for data fitting. The obtained results highlight the effectiveness of the proposed approach in correlating fibers structure with composite material mechanics.",
keywords = "Crimped fibers, Multiscale homogenization, Soft connective tissues, Structure-mechanics relationship, Undulated yarn",
author = "Michele Marino and Peter Wriggers",
note = "Funding information: A postdoctoral fellowship from the Alexander von Humboldt Foundation for M. Marino is gratefully acknowledged. The authors kindly acknowledge Giuseppe Vairo for fruitful discussions on the paper.",
year = "2016",
month = jun,
day = "9",
doi = "10.1016/j.jmps.2016.05.010",
language = "English",
volume = "98",
pages = "429--453",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Ltd.",
}