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7 - Constitutive Formulations for Network Materials

Published online by Cambridge University Press:  15 September 2022

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

A review of current constitutive formulations for Network materials is presented in this chapter. Network materials are composed from discrete elements and are not continua. Their behavior is somewhat similar to that of mechanisms. Furthermore, deformation is generally nonaffine due to the stochastic network structure. These observations render difficult the adaptation of classical constitutive equations for this class of materials. These issues are discussed in detail in the opening section. Further, the chapter is divided into four sections, each presenting models of a certain type. The first category includes phenomenological models defined based on a free energy functional and examples relevant for thermal networks (elastomers and gels) are presented. The next three categories encompass mechanism-based models, which are divided based on the degree to which the respective models account for nonaffinity in affine, quasi-affine, and nonaffine models. An outline of the challenges and opportunities related to the development of mechanism-based constitutive models for Network materials is presented in closure.

Keywords

constitutive modelhyperelasticelastic–plasticmicropolaraffine modelsunit cell modelsrubber elasticitymicrosphere modelmultiscale model
Type
Chapter
Information
Network Materials
Structure and Properties
 , pp. 252 - 277
Publisher: Cambridge University Press
Print publication year: 2022

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