Abstract
Viscoelastic materials induce delayed mechanical response when loaded, and are of major interest for designing damping systems or for studying the creep behavior in concrete, among many other engineering applications. Progress in the design of viscoelastic composites require the construction of homogenized models based on microstructural analysis. As compared to the homogenization problems presented in the previous chapters, an additional difficulty arises from the time dependence of the behavior of the individual phases. In this chapter, a method for computing the homogenized behavior of linear viscoelastic materials is presented, based on the work proposed in [1]. The technique operates in the time domain. In this book, we restrict ourselves to this method due to its simplicity, even though other approaches have been proposed based on Laplace–Carson transform. A literature review about the different available methods and their drawbacks/advantages can be found in [1].
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Tran AB, Yvonnet J, He Q-C, Toulemonde C, Sanahuja J (2011) A simple computational homogenization method for structures made of heterogeneous linear viscoelastic materials. Comput Methods Appl Mech Eng 200(45–46):2956–2970
Schiff JL (2013) The Laplace transform: theory and applications. Springer Science & Business Media, Berlin
Simo JC, Hugues TJR (1998) Computational inelasticity. Springer, Berlin
Kurnatowski B, Matzenmiller A (2008) Finite element analysis of viscoelastic composite structures based on a micromechanical material model. Comput Mater Sci 43(4):957–973
Taylor RL, Pister KS, Goudreau GL (1970) Thermomechanical analysis of viscoelastic solids. Comput Methods Appl Mech Eng 2(1):45–59
Hashin Z (1965) Viscoelastic behavior of heterogeneous media. J Appl Mech 32:630–636
Hashin Z (1970) Complex moduli of viscoelastic composites - I. general theory and application to particulate composites. Int J Solids Struct 6:539–552
Feyel F (1999) Multiscale FE\(^2\) elastoviscoplastic analysis of composite structure. Comput Mater Sci 16(1–4):433–454
Tran AB, Yvonnet J, He Q-C, Toulemonde C, Sanahuja J (2013) A four-scale homogenization analysis of creep of a nuclear containment structure. Nucl Eng Des 265:712–726
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Yvonnet, J. (2019). Linear Viscoelastic Materials. In: Computational Homogenization of Heterogeneous Materials with Finite Elements. Solid Mechanics and Its Applications, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-030-18383-7_7
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DOI: https://doi.org/10.1007/978-3-030-18383-7_7
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