We study associating polymer gels under steady shear using Brownian dynamics simulation to explore the interplay between the network structure, dynamics, and rheology. For a wide range of flow rates, we observe the formation of shear bands with a pronounced difference in shear rate, concentration, and structure. A striking increase in the polymer pressure in the gradient direction with shear, along with the inherently large compressibility of the gels, is shown to be a crucial factor in destabilizing homogeneous flow through shear-gradient concentration coupling. We find that shear has only a modest influence on the degree of association, but induces marked spatial heterogeneity in the network connectivity. We attribute the increase in the polymer pressure (and polymer mobility) to this structural reorganization. DOI: 10.1103/PhysRevLett.119.117801 Associating polymers (APs) in dilute solution can aggregate into multichain clusters when the "sticker" (the physically associating moiety) attraction energy exceeds the thermal energy kT. Near the overlap concentration, sticker clusters can be bridged by polymer strands and form an interconnected volume spanning networka physical gel [1][2][3]. Such gels are found in both natural and synthetic systems, and display a striking array of rheological behavior, including strain stiffening [4], negative normal stresses [5], shear thickening [6,7], shear thinning [8], and shear banding [9][10][11][12][13][14][15].Despite the ubiquity and versatility of physical gels, a fundamental understanding of the interplay between their microstructure, dynamics, and rheological properties remains a challenging and open problem. For instance, while experiments and simulations of associative networks (including both AP [13][14][15] and colloidal [16] gels) under simple shear have observed spatial inhomogeneities in both shear rate and density, suggesting some form of sheargradient concentration coupling (SCC) [17][18][19][20], the microscopic mechanism for the instability is unclear. Mean-field based models [21] of AP rheology have largely focused on chain elasticity and have not accounted for density inhomogeneity (e.g., chain migration) which would require a constitutive relation describing the solute pressure (the driving force for chain migration) as a function of shear rate and concentration. To date, no such relation has been explored for physical gels-largely due to the experimental difficulty in measuring the pressure of a single species in solution under shear [22]. Furthermore, the observation of SCC in both AP and colloidal gels suggests that the common physics between the gels-such as network connectivity and transient particle localization-may play a key role in driving the instability.In this Letter, we report results from Brownian dynamics simulations of an AP gel under steady shear in the nonlinear, shear-thinning, regime. The polymers we study have multiple associating sticker groups along the backbone, a prevalent building block of natural and synthetic gels. Our stud...