Microscopic theory of nonequilibrium stress relaxation and residual stress after flow cessation in ultra-dense colloidal suspensions

Re-solidification after nonlinear shear cessation of dense suspensions fluidized via a solid-fluid yielding transition is a poorly understood fundamental problem of high applications relevance (e.g., 3D printing, materials processing). For ultra-dense glass-forming hard sphere colloidal suspensions, key questions include the role of strain rate, strain (or elapsed time) when shear is terminated, and packing fraction on the coupled nonequilibrium relaxation of stress and microstructure and the emergence of unrelaxed residual stress. We have created a microscopic statistical mechanical theory for this problem by combining the Elastically Collective Nonlinear Langevin Equation theory of the elastic modulus and activated structural relaxation time under both quiescent and mechanically nonequilibrium conditions with a new self-consistent description of transient rheology and deformation-modified microstructure. With increasing packing fraction, distinctive temporal stress relaxation responses are predicted ranging from exponential, to stretched exponential, to slow fractional power-law decay with nonuniversal exponents. Apparent residual stresses on experimental time scales are predicted as the glassy solid re-forms. The theory is in good accord with experiments.