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affine deformation

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5 - Affine Deformation
Catalin R. Picu, Rensselaer Polytechnic Institute, New York
Book:

Network Materials

Published online:

15 September 2022

Print publication:

22 September 2022, pp 128-145
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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.