Nonlinear viscoelasticity plays a pivotal role in various phenomena spanning the geodynamic spectrum, including tidal flexures of planets and moons, mantle convection, and the propagation of seismic waves. Years of meticulous observations on the deformation of geological materials in laboratory settings have contributed to characterizing various aspects of this intricate behavior. These findings highlight the importance of numerous microscale processes that impact the nonlinearity of the macroscopic variables under observation. Such microscale processes include dynamic changes in grain sizes of polycrystalline materials during deformation, grain orientation, various types and quantities of defects in the crystalline structure, and more. Addressing and integrating these findings into large-scale geodynamic problems is not trivial, given the potential for over 10 orders of magnitude difference between the dynamics of geodynamic phenomena and microstructural dynamics. To address this, an intermediate step involving the use of a mechanistic model to bridge the gap between laboratory findings and large-scale parameterizations is proposed. The mechanistic model allows for the adjustment and optimization of parameters using data from laboratory measurements, thereby capturing essential dynamics at the macroscopic scale. This mechanistic model can then serve as a reference for large-scale modeling. The endeavor behind this work is to develop, optimize, and validate a mechanistic model for nonlinear viscoelasticity tailored to geological materials. We incorporate and parameterize microscale processes within a set of differential equations, assessing their capability to capture dynamics across a range of experiments involving ice and olivine. Furthermore, we demonstrate the adaptability of the model to different deformation conditions, presenting results in both time and frequency domains. Leveraging data-driven Markov Chain Monte Carlo (MCMC) methods for optimization, we propose a framework applicable to diverse experimental datasets. Furthermore, we explore specific geodynamic scenarios that could benefit from the application of this new model.