A generalized time-domain constitutive finite element approach for viscoelastic materials
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Date
2024-04-01
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Published version
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Citation
E. Abercrombie, J. Gregory McDaniel, T. Walsh. 2024. "A generalized time-domain constitutive finite element approach for viscoelastic materials" Modelling and Simulation in Materials Science and Engineering, Volume 32, Issue 3, pp.035028-035028. https://doi.org/10.1088/1361-651x/ad2ba1
Abstract
Despite the existence of time domain finite element formulations for viscoelastic materials, there are still substantial ways to improve the analysis. To the authors’ knowledge, the formulation of the problem is always done with respect to a single constitutive relation and so limits the implementer to a single scheme with which to model relaxation. Furthermore, all current constitutive relations involve the finding of fitting parameters for an analytical function, which is a sufficiently painful process to warrant the study of best fitting procedures to this day. In contrast, this effort is the first full derivation of the two dimensional problem from fundamental principles. It is also the first generalization of the problem, which frees users to select constitutive relations without re-derivation or re-expression of the problem. This approach is also the first approach to the problem that could lead to the elimination of constitutive relations for representing relaxation in viscoelastic materials. Following, the full derivation, several common constitutive relations are outlined with analysis of how they may best be implemented in the generalized form. Several expressions for viscoelastic terms are also provided given linear, quadratic, and exponential interpolation assumptions.
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© 2024 The Author(s). Published by IOP Publishing Ltd. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.