Look at the equations in N.V. Brilliantov, N. Albers, F. Spahn and T. Poschel : "Collision dynamics of granular particles with adhesion", PRE 76, 051302 /1 - 12 (2007)

applied to the normal impact of two identical spheres. MYL 8/3/08

notation:
ff	penetration distance function of contact radius
a	contact radius
d	D = (3/2)(1-\nu^2)/Y [Pa^(-1)]
\nu	Poisson's ratio
Y	Young's modulus (Pa)
g	surface energy (J/m^2)
r	sphere radius (m)

Equation (11) p. 051302 - 2 for the penetration distance vs. contact radius:

ff[a_]:=a^2*2/r-Sqrt[8*Pi*g*d*a/3];

... and its derivative with respect to the contact radius a :

(∂_a) ff[a]

Find the minimum penetration distance :

Solve[-((d g (Sqrt[((2 π)/3)]))/(Sqrt[a d g]))+((4 a)/r)==0,a]

Simplify the cube of the contact radius at the minimum penetration distance :

((1/2) (d^(1/3)) (g^(1/3)) ((((π/3)))^(1/3)) (r^(2/3)))^3

Simplify the minimum (negative) penetration distance :

Simplify[ff[(1/2) (d^(1/3)) (g^(1/3)) ((((π/3)))^(1/3)) (r^(2/3))]]

Implement Eq. (12) p. 051302 - 2 for the force :

force[a_]:=2*a^3/d/r-Sqrt[6*Pi*g*a^3/d];

Simplify the force at the contact radius for the minimum penetration distance :

Simplify[force[(1/2) (d^(1/3)) (g^(1/3)) ((((π/3)))^(1/3)) (r^(2/3))]]

Differentiate the force vs. contact radius :

(∂_a) force[a]

Find the contact radius at minimum force :

Solve[-((3 (a^2) g (Sqrt[((3 π)/2)]))/(d (Sqrt[(((a^3) g)/d)])))+((6 (a^2))/(d r))==0,a]

Simplify the cube of the contact radius at the minimum force :

((1/2) (d^(1/3)) (g^(1/3)) (((3 π))^(1/3)) (r^(2/3)))^3

Simplify the minimum force :

Simplify[force[(1/2) (d^(1/3)) (g^(1/3)) (((3 π))^(1/3)) (r^(2/3))]]

Simplify[ff[(1/2) (d^(1/3)) (g^(1/3)) (((3 π))^(1/3)) (r^(2/3))]]

Conclusions : Brilliantov et al adopted a sepration force and contact radius that are different than in the JKR theory. In the latter, separation occurs at the minimum penetration distance, which is negative. Instead, Brilliantov et al assumed that separation occurs at the minimum force, which is negative.