Hello,
I believe there is an error in shear modulus formula in the manual for pair_gran. Instead of
1/G*=2(2+nu1)(1-nu1)/Y1+2(2+nu2)(1-nu2)/Y2
there should be
1/G*=2(2-nu1)(1+nu1)/Y1+2(2-nu2)(1+nu2)/Y2
If we take two equal materials so nu1=nu2=nu and Y1=Y2=Y then accordind to your formula G*=Y/[4(2+nu)(1-nu)] and k_t=8G*=2Y/[(2+nu)(1-nu)], however according to the literature, k_t=2Y/[(2-nu)(1+nu)].