Nonlinear Viscoelastic Model for Ice and Olivine, Constrained by Experimental Data using MCMC

Mechanisms of energy dissipation in ice and olivine have been studied experimentally in the past, with an observed strain-amplitude dependence that indicates nonlinear viscoelastic behavior resulting from the presence and motion of dislocations. In a range of low to moderate stress amplitudes, dislocations can ”bow out” between pinning points. If the resolved shear stress is sufficiently large, dislocations may escape their pinning points and elastically interact with each other. The transition from pinned to unpinned motion, along with the subsequent interactions and recovery processes, are associated with the shift from anelastic to steady-state viscous behavior. This transition forms the basis of a viscoelastic model. Despite the experimental evidence of nonlinear mechanisms, the availability of comprehensive nonlinear viscoelastic models for geological materials is limited. In this work, we propose a nonlinear viscoelastic model that captures the effect of dislocation dynamics on energy dissipation. The model is based on the well-known linear Burgers model, modified to incorporate non-linear steady-state viscous flow, and enhanced by the integration of fabric and grain-size evolution dynamics. The proposed model is tested against data from constant strain-rate and forced oscillation experiments, and the parameters are constrained using Markov Chain Monte Carlo (MCMC) methods. The model successfully reproduces data from deformation experiments in the dislocation creep regime and can be extended to experiments involving other deformation mechanisms as well.