A large deformation gradient theory for glassy polymers by means of micromorphic regularization

A. Hamdoun, R. Mahnken, Archive of Applied Mechanics 94 (2024) 1221–1242.

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Journal Article | Published | English
Abstract
<jats:title>Abstract</jats:title><jats:p>Cold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization.</jats:p>
Publishing Year
Journal Title
Archive of Applied Mechanics
Volume
94
Issue
5
Page
1221-1242
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Hamdoun A, Mahnken R. A large deformation gradient theory for glassy polymers by means of micromorphic regularization. Archive of Applied Mechanics. 2024;94(5):1221-1242. doi:10.1007/s00419-024-02570-0
Hamdoun, A., & Mahnken, R. (2024). A large deformation gradient theory for glassy polymers by means of micromorphic regularization. Archive of Applied Mechanics, 94(5), 1221–1242. https://doi.org/10.1007/s00419-024-02570-0
@article{Hamdoun_Mahnken_2024, title={A large deformation gradient theory for glassy polymers by means of micromorphic regularization}, volume={94}, DOI={10.1007/s00419-024-02570-0}, number={5}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Hamdoun, Ayoub and Mahnken, Rolf}, year={2024}, pages={1221–1242} }
Hamdoun, Ayoub, and Rolf Mahnken. “A Large Deformation Gradient Theory for Glassy Polymers by Means of Micromorphic Regularization.” Archive of Applied Mechanics 94, no. 5 (2024): 1221–42. https://doi.org/10.1007/s00419-024-02570-0.
A. Hamdoun and R. Mahnken, “A large deformation gradient theory for glassy polymers by means of micromorphic regularization,” Archive of Applied Mechanics, vol. 94, no. 5, pp. 1221–1242, 2024, doi: 10.1007/s00419-024-02570-0.
Hamdoun, Ayoub, and Rolf Mahnken. “A Large Deformation Gradient Theory for Glassy Polymers by Means of Micromorphic Regularization.” Archive of Applied Mechanics, vol. 94, no. 5, Springer Science and Business Media LLC, 2024, pp. 1221–42, doi:10.1007/s00419-024-02570-0.

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