The response to large amplitude oscillatory shear of a soft colloidal glass formed by a suspension of multiarm star polymers is investigated by means of well-defined continuous local measures. The local measures provide information regarding the transient elastic and viscous response of the material, as well as elastic extension via a shifting equilibrium position. It is shown that even when the amplitude of the strain is very large, cages reform and break twice per period and exhibit maximum elasticity around the point of zero stress. It is also shown that around the point of zero stress, the cages are extended by a nearly constant amount of approximately 5 at 1 rad/s and 7 at 10 rad/s, even when the total strain is as large as 420. The results of this study provide a blueprint for a generic approach to elucidating the complex dynamics exhibited by soft materials under flow.
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