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For decades, scientists have observed, but been unable to explain, a phenomenon seen in some soft materials: When force is applied, these materials exhibit not one, but two spikes in energy dissipation, known as overshoots. Because overshoots are generally thought to indicate the point at which a material yields, or transitions from solid-like to fluid-like behavior, the dual response was therefore assumed to indicate "double yielding"—the idea that to fully fluidize a material, it needed to yield twice.

Now, researchers at the University of Illinois Urbana-Champaign have shown that this behavior is different than previously hypothesized. Their paper, "," is published in Â鶹ÒùÔºical Review Letters.

In the study, chemical and biomolecular engineering professor Simon A. Rogers and his team, led by then-graduate student James J. Griebler show that the two-step response is the result of two independent processes: first, a softening of the material's elastic structure, and later, true yielding.

For their work, the team used a novel approach called recovery rheology, which considers strain—the measure of how much a material deforms—to be a composite parameter consisting of recoverable and unrecoverable components. Rogers likened it to chewing gum.

"Imagine you were chewing gum and pulled it out of your mouth, and you stretched it," he explained. "Some of it will stretch and, if you let it go, some of it will recoil—it'll spring back a little, but it won't spring back all the way. That little bit of recoil is what we call the recoverable part, and the fact that it doesn't come all the way back is the unrecoverable part."

Using this concept as their starting point, the researchers conducted a series of oscillatory shear experiments using Carbopol, a gel-like polymer dissolved in propylene glycol that is widely found in many commercial gel products. As they increased the strain, the material exhibited two distinct overshoots in its response.

Then, by observing how much of the applied deformation was recoverable and how much was unrecoverable, they observed that these overshoots stemmed from separate physical processes rather than a repeated one. The first, smaller overshoot indicated material softening without yielding—a reversible behavior.

In contrast, the second, more pronounced overshoot marked a transition to full yielding, representing an irreversible deformation. The team supported their findings with development of a predictive model that accurately captures this double overshoot behavior.

While the immediate impact of their work lies primarily in advancing future research, distinguishing between double yielding and distinct physical processes could eventually influence how materials are handled in industrial applications.

"Processing these materials involves large and rapid deformations that take the materials out of equilibrium," Rogers said. "What our model does is provide a more accurate description of that out-of-equilibrium behavior, so we better understand how the materials respond under the conditions we actually care about."

Rogers, whose background in physics often leads him to approach rheological problems in non-traditional ways, said the study also highlights the value of careful experimentation over purely theoretical approaches.

"For the longest time, people tried solving this problem by performing the same experiments that were used to discover the effect and they thought that the answer was going to be somewhere in a mathematical analysis," Rogers said.

"What we showed is that simple experiments designed to test the underlying hypotheses are worth much more than that complex mathematical analysis, and they pointed us towards a reality that hadn't previously been discovered."

In addition to Rogers and Griebler, who is now a postdoctoral researcher at the University of Tennessee, co-authors include visiting scholar Anita S. Dobo and undergraduate researcher Elizabeth E. Miczuga.