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Analytical Approach to Quantifying the Non-Affine Behavior of Fiber Networks

Published online by Cambridge University Press:  01 February 2011

Hamed Hatami-Marbini  and
Catalin Picu
Hamed Hatami-Marbini
Affiliation:
Rensselaer Polytechnic Institute, Department of Mechanical Engineering, 110 15th St., Troy, NY, 12180, United States
Catalin Picu
Affiliation:
picuc@rpi.edu, Rensselaer Polytechnic Institute, Troy, NY, 12180, United States
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Abstract

Fiber networks deform nonaffinely due to their inhomogeneous structure. The degree of nonaffinity depends on many factors such as the spatial distribution and properties of fibers, the nature of the applied load, the type of joints and the length scale of observation. The “homogenized” response on given scale depends on the non-affine mechanics on all sub-scales. Here, a method is developed to map the non-affine mechanics of a regular network with a large density of defects into an equivalent continuum, which is then used to determine the homogenized elastic properties of the network. This semi-analytic method establishes a relationship between the structure of the network and its overall elastic properties. Furthermore, we develop a method to quantify the nonaffine strains in a random network and use it to study the dependence of the degree of non-affinity to the scale of observation as well as the dependence on the network architecture.

Keywords

fiberstress/strain relationshipstructural
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1060: Symposium LL – Bioinspired Polymer Gels and Networks , 2007 , 1060-LL09-03
Copyright
Copyright © Materials Research Society 2008

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