Surface stress can take over the role of bulk elasticity in resisting deformation due to adhesion between particles, replacing JKR theory.  Here are some of our contributions:

Xu, Xuejuan, Anand Jagota, and Chung-Yuen Hui. “Effects of surface tension on the adhesive contact of a rigid sphere to a compliant substrate.” Soft matter 10, no. 26 (2014): 4625-4632.

Hui, Chung-Yuen, Tianshu Liu, Thomas Salez, Elie Raphael, and Anand Jagota. “Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion.” Proc. R. Soc. A 471, no. 2175 (2015): 20140727.