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\begin{document}

\title{Andrade rheology in planetary science}



\author[1]{Michaela Walterová}%
\author[2]{Ana-Catalina Plesa}%
\author[3]{Frank W. Wagner}%
\author[2]{Doris Breuer}%
\affil[1]{DLR Institute of Planetary Research}%
\affil[2]{German Aerospace Center}%
\affil[3]{Jülich Supercomputing Center, Forschungszentrum Jülich (FZJ}%


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  \date{May 26, 2024}


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\begin{abstract}
The anelastic reaction of planet-forming materials is successfully
described by the Andrade rheological model, which presents an extension
of the simple Maxwell rheology. In addition to the instantaneous elastic
deformation and the long-term viscous creep, the Andrade rheology
incorporates the transient creep in metals, ices, and silicates, and is
able to explain the tidal parameters of planets even in cases, where the
Maxwell model requires the assumption of unrealistically low mantle
viscosities. In this work, we discuss the applications of the Andrade
model in planetary science, the parameters used in the literature, and
their justification by material science and geodesy. We also examine the
topic of relating the empirical tidal parameters to the mantle viscosity
of moons and terrestrial planets and assess the limitations resulting
from the uncertainties in the rheological parameters. Our study
illustrates the necessity for future measurements that would help to
better calibrate the rheological models to conditions relevant to the
deep interiors of planets and moons.%
\end{abstract}%



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