In this talk I will discuss our recent results on the microscopic physical origins of nonlinear mechanical states in two vastly different materials: colloidal suspensions and active gels. In the first part of my talk, I will introduce a method we have developed that allows us to resolve the spatial distribution of stresses in sheared soft-materials. We apply this technique to suspensions that undergo dynamical phase transitions in response to external stimuli. I will present our results on the existence of clearly defined dynamically localized regions of substantially increased stress that appear intermittently at stresses well above the applied stress. Surprisingly, we find that these spatially distinct and dynamic phases account quantitatively for the observed shear thickening seen in sheared colloidal dispersions. In the second part of my talk I will discuss our results on the flow of active matter. Our system is composed of microtubules and kinesin motor proteins that self-assemble to form complexes that propel themselves through the fluid. What results is a localization of elasticity that depends on the rate of applied shear and the internal timescales of dynamic reorganization.
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