How can shear loading rate affect the soft adhesive contact area?

Figure 1: On the soft finger on spoon contact [1]

Today, my youngest daughter dropped her spoon again on the floor. She didn’t do it on purpose. But I still had to get it back again, give it a quick wash again and give it back again… What’s wrong? It’s not that hard to hold it well!

But maybe it is. According to Papangelo [2], the adhesive soft contact (as in finger pulp on spoon contact) behaviour is dependent on shear rate, and the relationship is clearly not linear. A child of her age learns which grasping force is relevant for which object under different conditions. As a result she might simply be surprised because the contact behaviour varies in a non-linear manner relative to the shear loading rate (although not being aware of the nature of this complex interaction). So, maybe it is hard to hold it well!

Let’s dive into Papangelo [2] work to figure out what are the contact behaviour challenges at stake. While the literature on the topic seems rather prolific, the shear loading rate influence on the contact area shrinking has not been studied so far. In the study, the normal load is null, so the non-zero contact area is due to the adhesion forces. Before the contact completely slips, the contact area shrinks until it reaches a threshold value. At this specific threshold, the whole contact area and the two bodies slip (and the spoon falls down!).

Whereas soft material properties are often rate dependent, the theoretical and experimental studies on the topic always considered a fixed loading rate. Therefore, Papangelo [2] proposes a theoretical model of the sphere on plane contact which considers this loading rate dependence. To develop his analysis, the sliding region is considered like a crack and the fracture mechanics theoretical tools are used to describe the progression of the sliding region within the contact (as proposed by Johnson et al. in 1971 [3]). The other main theoretical input is the law describing adhesion: it takes into account the velocity of the surface separation with a well accepted formula. The fracture mechanics theory introduced considers energy and work balance and allows for describing the shear occuring in the different contact regions (see Figure 2) that lead to contact area shrinking.

Figure 2: Sliding and sticking regions within the contact area

After mathematical developments, Papangelo [2] proposes a set of analytical expressions to describe the contact area (A) and the surface energy. The expressions are defined as dependent on the material properties, the surface properties and also the shear loading rate (dT/dt). It turns out that a fast loading leads to a small contact area reduction before sliding (see Figure 3). However, as you get closer to the quasi-static loading, the contact area shrinking becomes more and more important. The author also uses the formulae to study the influence of the surface adhesion properties on the contact area shrinking.

Figure 3: Contact area (A) variations during tangential loading (T) for different loading rates (dT/dt) – dashed line being the gross sliding condition

Ideally, the shear rate dependence of the body bulk properties should also be included in the model, but the non linearity of the adhesion properties already brings further the knowledge on the soft adhesive contacts. While it is true that experimental results are sought to assess the formulae developed, this new set of analytical tools already showed their interest.

To conclude, I don’t think that this shear loading rate dependency of the contact behaviour impacts the object grasping learning curve. At first I thought that the twitchy movements of a kid could generate a large loading rate and make the contact slip earlier than expected. But actually a large loading rate makes the slip occur at a larger energy level… I guess the friction coefficient difference between sliding and sticking condition plays a bigger role. Or maybe learning just takes time, and it is fine this way!

Feel free to read the full article if you have enjoyed reading this blog.

[1] Photo by Providence Doucet on Unsplash

[2] Papangelo, Antonio. (2021). On the Effect of Shear Loading Rate on Contact Area Shrinking in Adhesive Soft Contacts. Tribology Letters. 69.

[3] Johnson, K. L., Kendall, K. & Roberts, A. D. 1971 Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313.

About Jean-David Wheeler 13 Articles
After a PhD thesis with SKF at the INSA de Lyon - LaMCoS dedicated to the lubrication of large size roller bearings, Jean-David joined SIMTEC ( to continue helping industries to develop their processes and products.

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