We show experimentally that multiple soft glassy fluids are capable of storing directional rheological signatures from past shear history, evidenced during stress growth and overall nonmonotonic stress relaxation after small steps in strain. We illustrate theoretically that these responses can be reproduced without requiring thixotropy or shear banding, which are typically implicated in time-dependent rheological complexities. Instead, we use a simple elastoplastic rheological model with power-law yielding that incorporates a distribution of local strain states. Using insight from the model, we suggest a mechanism for the experimentally observed stress increase to be driven by residual anisotropy in strain states that are relaxed at different rates. We demonstrate that these effects persist even after material is stressed beyond the yield stress, indicating that past deformation may have more influence than previously thought.

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• Non-Newtonian fluids
• Plastic deformation
• Rheology
• Foams
• Gels