A Taylor–Leibniz expansion for time domain viscoelastic studies
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Date
2025-03-15
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Published version
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Citation
E. Abercrombie, J.G. McDaniel. 2025. "A Taylor–Leibniz expansion for time domain viscoelastic studies" Modelling and Simulation in Materials Science and Engineering, Volume 33, Issue 2, pp.025003-025003. https://doi.org/10.1088/1361-651x/ada175
Abstract
Transient simulations of viscoelastic materials remain common, as does interest in the formulation of such simulations. This paper offers an alternative to the current set of solution schemes, including the Newmark-Beta or space-time Galerkin methods. The solution to an equation of motion for a viscoelastic simulation can be expressed by a Taylor series, when a Leibniz integration rule is applied to the time integral appearing in the viscoelastic stress equation. The result is a remarkably simple scheme to implement that also offers extremely rapid solution times. This effort includes a formulation of the approach, as well as numerical results for a simple mass and viscoelastic spring system, including an assessment of the number of Taylor series terms needed to accurately depict transient behavior. The paper outlines how the approach could be extended to finite element analysis and how complex loading conditions could be accounted for. Care is given in addressing the potential limitations of the approach.
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© 2025 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.