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Fractional-order relaxation laws in non-linear viscoelasticity

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Abstract

Viscoelastic constitutive equations are constructed by assuming that the stress is a nonlinear function of the current strain and of a set of internal variables satisfying relaxation equations of fractional order. The dependence of the relaxation equations on the strain can also be nonlinear. The resulting constitutive equations are examined as mapping between appropriate Sobolev spaces. The proposed formulation is easier to implement numerically than history-based formulations.

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  1. Department of Geosciences, Princeton University, 321B Guyot Hall, Princeton, NJ, 08544, USA

    Andrzej Hanyga

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  1. Andrzej Hanyga
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Communicated by J.-J. Marigo

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Hanyga, A. Fractional-order relaxation laws in non-linear viscoelasticity. Continuum Mech. Thermodyn. 19, 25–36 (2007). https://doi.org/10.1007/s00161-007-0042-0

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