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Viscoelastic stress relaxation is a basic characteristic of soft mattersystems such as colloids, gels, and biological networks. Although the Maxwellmodel of linear viscoelasticity provides a classical description of stressrelaxation, the Maxwell model is often not sufficient for capturing the complexrelaxation dynamics of soft matter. In this Tutorial, we introduce and dis-cussthe physics of non-Maxwellian linear stress relaxation as observed in softmaterials, the ascribed origins of this effect in different systems, andappropriate models that can be used to capture this relaxation behavior. Weprovide a basic toolkit that can assist the understanding and modeling of themechanical relaxation of soft materials for diverse applications.

Non-Maxwellian viscoelastic stress relaxations in soft matter