At high temperature and/or low strain rates, a relative sliding of adjacent grains may be accommodated by the diffusion of atomic species along the grain boundaries. Such diffusion-aided grain boundary sliding- (GBS) phenomenon is commonly referred to as Coble creep [1]. In recent years, Coble creep has gained increasing attention in the field of geodynamics, as it may provide key insights into deformation processes occurring within the ductile-to-brittle transition (BDT) zone [2,3]. Understanding these mechanisms improves our understanding of the conditions leading to the onset of earthquakes initiating nearby the BDT zone. The present study addresses the numerical modeling of Coble creep, with particular emphasis on the threshold shear stress allowing viscous GBS. Classical models of Coble creep assumed a linear, Newtonian viscous law relating tangential velocity mismatch to the shear stresses acting on GBs. However, recent experimental observations suggest a non-Newtonian viscous regime for GBS [4,5]. Building on previous work [6], we propose an original variational approach [7] to model coupled GBS and grain boundary diffusion in periodic aggregates with irregular polycrystal topologies in two dimensions. The proposed numerical framework enables a systematic investigation of the influence of macroscopic loading conditions on the activation of sliding in GBs. Increasing the applied macroscopic stress mobilizes a larger fraction of GBs, which lowers the macroscopic viscosity. A particular emphasis is placed on comparing microstructures composed of equiaxed grains with those containing elongated grains. Differences are observed in the statistics of grain rotations and the respective contributions of GBS and grain boundary diffusion in achieving macroscopic deformation.