  We propose a simple model comprising three particles to study the nonlinear
mechanical response of jammed frictional granular materials under oscillatory
shear. Owing to the introduction of the simple model, we obtain an exact
analytical expression of the complex shear modulus for a system including many
mono-dispersed disks, which satisfies a scaling law in the vicinity of the
jamming point. These expressions perfectly reproduce the shear modulus of the
many-body system with low strain amplitudes and friction coefficients. Even for
disordered many-body systems, the model reproduces results by introducing a
single fitting parameter.
