A formula for simulating softness

US researchers say they have developed a formula for accurately simulating softness, opening the way to create more realistic touch sensations in electronic skin, prostheses or medical robotics.

Writing in the journal Science Advances, a team of engineers and psychologists from the University of California San Diego describe experiments that led to the development of equations that can calculate how soft or hard a material will feel based on material thickness, Young’s modulus (a measure of a material’s stiffness), and micropatterned areas. 

They can also do the reverse and calculate, for example, how thick or micropatterned a material needs to be to feel a certain level of softness.

“We found an explicit relationship between the perceived softness of an object and its geometric properties,” the authors write. “Using this approach, it is possible to design objects for human interaction with a desired level of perceived softness.”

“What’s interesting about this,” adds Charles Dhong, who co-led the study with Darren Lipomi, “is that we’ve found two new ways to tune the perceived softness of an object – micropatterning and changing the thickness. 

“Young’s modulus is what scientists typically turn to in terms of what’s soft or hard. It is a factor, but now we show that it’s only one part of the equation.”

Dhong, Lipomi and colleagues began by examining two parameters engineers use to measure a material’s perceived softness: indentation depth (how deep a fingertip presses into a material) and contact area between the fingertip and the material. 

These usually change simultaneously as a fingertip presses into an object. To better understand how each independently affects the perception of softness, the researchers engineered materials that decoupled the two, then tested them on human subjects.

They created nine different slabs of elastic material, each with its own unique ratio of indentation depth to contact area. The slabs differed in amount of micropatterning on the surface, thickness and Young’s modulus.

Micropatterning describes arrays of tiny raised pillars that allow a fingertip to press deeper without changing the contact area, much like a Pinscreen toy, where arrays of pins slide in and out to make a 3D impression.

The slabs allowed participants to move freely during testing, the researchers say, which closely mimicked how humans explore surfaces in real life.

Fifteen subjects were asked to identify the softer slab each time they were presented with a pair, and to rank the nine slabs from softest to hardest.

Overall, the slabs perceived as softer were thicker, had little to no micropatterning on the surface, and had a low Young’s modulus. 

This allowed the researchers to develop a series of conclusions they say may inform basic studies on the sense of touch.

Among them was the “interesting” realisation that the perception of softness is a basic sensation, not a combination of other sensations.

“This means softness is a primary ingredient of the human sense of touch. It’s like how we have RGB for colour displays,” Lipomi said. 

“If we can find the other ‘pixels of touch,’ can we combine them to make any tactile image we want? These are the fundamental things we would like to know going forward.”