Solids deform and fluids flow, but soft glassy materials, such as emulsions,foams, suspensions, and pastes, exhibit an intricate mix of solid andliquid-like behavior. While much progress has been made to understand theirelastic (small strain) and flow (infinite strain) properties, suchunderstanding is lacking for the softening and yielding phenomena that connectthese asymptotic regimes. Here we present a comprehensive framework forsoftening and yielding of soft glassy materials, based on extensive numericalsimulations of oscillatory rheological tests, and show that two distinctscenarios unfold depending on the material's packing density. For densesystems, there is a single, pressure-independent strain where the elasticmodulus drops and the particle motion becomes diffusive. In contrast, forweakly jammed systems, a two-step process arises: at an intermediate softeningstrain, the elastic and loss moduli both drop down and then reach a new plateauvalue, whereas the particle motion becomes diffusive at the distinctly largeryield strain. We show that softening is associated with an extensive number ofmicroscopic contact changes leading to a non-analytic rheological signature.Moreover, the scaling of the softening strain with pressure suggest theexistence of a novel pressure scale above which softening and yieldingcoincide, and we verify the existence of this crossover scale numerically. Ourfindings thus evidence the existence of two distinct classes of soft glassymaterials -- jamming dominated and dense -- and show how these can bedistinguished by their rheological fingerprint.
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