Affine Deformation

Catalin R. Picu

doi:10.1017/9781108779920.006

5 - Affine Deformation

Published online by Cambridge University Press: 15 September 2022

Catalin R. Picu

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Catalin R. Picu: Affiliation:
Rensselaer Polytechnic Institute, New York

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Summary

Affine models have been used traditionally to describe the deformation of networks. Due to their prevalence, this chapter is dedicated to the review of such formulations. The chapter begins with a brief review of finite kinematics of continua and the definition of stress measures. Further, the affine deformation is defined and several parameters used to quantify the degree of nonaffinity are introduced. An expression is derived to quantify the evolution of preferential fiber orientation during affine deformation. Several constitutive models based on the affine deformation assumption are discussed: The affine models for molecular networks of flexible and semi-flexible filaments, and the affine model for athermal networks. The stress–optical law is reviewed, and its relation to the affine deformation models is discussed.

Keywords

kinematics affine deformation nonaffinity affine models thermal networks athermal networks semiflexible filament networks

Type: Chapter
Information: Network Materials
Structure and Properties
, pp. 128 - 145

DOI: https://doi.org/10.1017/9781108779920.006 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2022

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5 - Affine Deformation

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