The Effect of Nonlinear Viscoelasticity on Planetary Love Numbers

The planetary Love number is a dimensionless parameter representing the deformation response of a planet
to stress (Love, 1927). In its original formalism, the Love number was defined for pure elastic deformations,
but this definition was later extended to linear viscoelastic deformations using the Correspondence Principle
(Peltier, 1974). Currently, there are multiple methods for calculating planetary Love numbers that can
incorporate advanced rheological models (Henning and Hurford, 2014; Renaud and Henning, 2018; Melini
et al., 2022), yet all of these methods require that the rheology will be limited to linear viscoelasticity.
On the other hand, laboratory studies of attenuation on different geological materials suggest a nonlinear
viscoelastic behavior due to the movement of dislocations within the lattice (Gueguen et al., 1989; McCarthy
and Cooper, 2016). At high enough stresses, dislocations can escape pinning points and interact with
each other (Gremaud, 2009), leading to permanent deformations and attenuation that is dependent on
the amplitude of the oscillations. In this work, we are taking the first step into incorporating nonlinear
viscoelasticity in the calculation of planetary Love numbers. Assuming a homogeneous, incompressible,
self-gravitating sphere with nonlinear rheology, we are using a numerical scheme to calculate the complex
Love number. The results of the numerical model are then compared to the known analytical solutions for
the linear case.