sentences:  Note that this force is independent of the moduli of the two spheres.However, there is another possible solution for the value of formula_23 at this load.This is the critical contact area formula_185, given by
  
  If we define the work of adhesion as
  
  where formula_188 are the adhesive energies of the two surfaces and formula_189 is an interaction term, we can write the JKR contact radius as
  
  The tensile load at separation is
  
  and the critical contact radius is given by
  
  The critical depth of penetration is
  
  The Derjaguin-Muller-Toporov (DMT) model is an alternative model for adhesive contact which assumes that the contact profile remains the same as in Hertzian contact but with additional attractive interactions outside the area of contact.