Universal Relationship between Linear Viscoelasticity and Nonlinear Yielding in Soft Materials

The nonlinear response of yield stress fluids remains difficult to predict and control. Here, we show that the height of the overshoot in the loss modulus G^{''}, a key characteristic of yielding, depends only on linear viscoelastic properties. Furthermore, the position of this overshoot depends on linear viscoelastic and flow properties, demonstrating the important and enduring role of elasticity in yielding. The physics governing linear viscoelasticity is therefore not only preserved during yielding but also controls two commonly reported yielding metrics.