The transient structural and rheological behavior of soft glassy materials out of equilibrium is studied under small, medium, and large amplitude oscillatory shearing and interpreted via the fully quantitative sequence of physical processes (SPP) technique. We identify features of the local strain distribution that cause particular rheological responses and show that the SPP metrics accurately reflect the structural transitions. The SPP modulus is shown to reflect how much of the imposed strain is stored in the form of recoverable elastic strain, establishing it as an accurate measure of structural elasticity. We demonstrate the ability of the SPP scheme to accurately determine the amount of recoverable strain acquired in elastically dominated regimes by matching values estimated solely on the basis of the macroscopic stress to structural measures. In one case of large amplitude oscillatory shearing, the recoverable strain is shown to be around half a nondimensional strain unit by structural determination and from the SPP analysis, while the total imposed strain over the same interval is on the order of ten strain units. We therefore demonstrate the importance of separating the total and recoverable strains under strain-controlled conditions for the formation of accurate structure-property relations. We demonstrate how the alternating oscillatory state may be considered a consequence of a complex shear history. The results of this study show that the SPP scheme is a powerful tool for researchers wishing to understand the structural and rheological properties of soft glassy materials far from equilibrium.

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