Constitutive Equations for the Back Stress in Amorphous Glassy Polymers

by: Millard F Beatty

Mathematics and Mechanics of Solids, Vol. 10, No. 2. (1 April 2005), pp. 167-181.

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Abstract

Constitutive equations for the back stress in amorphous glassy polymers based on extended forms of the non-Gaussian James--Guth 3-chain and Arruda--Boyce 8-chain models of rubber elasticity are derived from the extended Wu and van der Giessen non-Gaussian full-network model. A simple and invariant constitutive equation for the back stress tensor is then derived from the Wu and van der Giessen model by an average-stretch approximation. Although the average-stretch model of the full-network amorphous microstructure is more general than other chain cell models, the constitutive equation is the same as the 8-chain back stress relation. Back stress equations for a class of extended phenomenological models, including the Gent material model, are described. 10.1177/1081286505036316

@article{citeulike:1551703, abstract = {Constitutive equations for the back stress in amorphous glassy polymers based on extended forms of the non-Gaussian James--Guth 3-chain and Arruda--Boyce 8-chain models of rubber elasticity are derived from the extended Wu and van der Giessen non-Gaussian full-network model. A simple and invariant constitutive equation for the back stress tensor is then derived from the Wu and van der Giessen model by an average-stretch approximation. Although the average-stretch model of the full-network amorphous microstructure is more general than other chain cell models, the constitutive equation is the same as the 8-chain back stress relation. Back stress equations for a class of extended phenomenological models, including the Gent material model, are described. 10.1177/1081286505036316}, author = {Beatty, Millard F. }, citeulike-article-id = {1551703}, doi = {10.1177/1081286505036316}, journal = {Mathematics and Mechanics of Solids}, keywords = {elasticity, polymers}, month = {April}, number = {2}, pages = {167--181}, posted-at = {2007-08-10 14:31:29}, priority = {2}, title = {Constitutive Equations for the Back Stress in Amorphous Glassy Polymers}, url = {http://dx.doi.org/10.1177/1081286505036316}, volume = {10}, year = {2005} }

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TY - JOUR ID - citeulike:1551703 L3 - citeulike-article-id:1551703 TI - Constitutive Equations for the Back Stress in Amorphous Glassy Polymers JF - Mathematics and Mechanics of Solids VL - 10 IS - 2 SP - 167 EP - 181 N2 - Constitutive equations for the back stress in amorphous glassy polymers based on extended forms of the non-Gaussian James--Guth 3-chain and Arruda--Boyce 8-chain models of rubber elasticity are derived from the extended Wu and van der Giessen non-Gaussian full-network model. A simple and invariant constitutive equation for the back stress tensor is then derived from the Wu and van der Giessen model by an average-stretch approximation. Although the average-stretch model of the full-network amorphous microstructure is more general than other chain cell models, the constitutive equation is the same as the 8-chain back stress relation. Back stress equations for a class of extended phenomenological models, including the Gent material model, are described. 10.1177/1081286505036316 KW - elasticity KW - polymers AU - Beatty, Millard PY - 2005/04/01/ UR - http://dx.doi.org/10.1177/1081286505036316 ER -

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