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Alternative finite strain viscoelastic models: constant and strain rate-dependent viscosity

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Abstract

In this study, we present alternative viscoelastic models for materials developing large strains. The novelty of these models is the definition of isochoric strain components, from which we numerically calculate isochoric strain rates. The proposed models differ from the most usual frameworks present in the literature, namely Köner–Lee decomposition models, hereditary integral models and thermodynamically consistent models. The last mentioned framework also uses the Flory’s multiplicative strain decomposition, but not in the same way proposed here. Our models are developed for solid mechanics and their time evolution is done through finite differences, simplifying the algorithmic tangent viscoelastic constitutive tensor and the consideration of strain rate-dependent viscosity. Using simple examples, we show that using finite difference for isochoric strain rate evolution does not introduce volumetric changes in purely distortional viscoelastic situations and vice versa. We also present examples related to experimental results, including nonlinear viscoelastic response. Finally, we present examples that show how viscoelastic materials with instantaneous response may not provide satisfactory damping for some structural sets and a comparison of our models with important classical models.

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Acknowledgements

This research has been supported by the São Paulo Research Foundation, Brazil - Grant #2020/05393-4 and Coordenação de Aperfeiçoamento de Pessoal de Ní­vel Superior - Brasil (CAPES) - Finance Code 001.

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  1. São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São Carlense, 400, São Carlos, SP, ZIP 13566-590, Brazil

    Eduardo Yuiti Hayashi & Humberto Breves Coda

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Hayashi, E.Y., Coda, H.B. Alternative finite strain viscoelastic models: constant and strain rate-dependent viscosity. Acta Mech (2024). https://doi.org/10.1007/s00707-024-03914-1

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