Cooperative-viscoplasticity theory based on overstress (C-VBO) theory proposed to cover the total time, temperature, and graphene fraction dependent mechanical behavior of the nanocomposite material is simplified in this work. The previous version of the VBO model for nanocomposites includes the agglomeration effect of nanofiller by dividing the polymer nanocomposite into two parts as "agglomerated" and "effective matrix" phases. In this work, to be able to define the behavior of nanocomposites when nanofiller is evenly distributed into the matrix, the material model is simplified by defining the bulk and shear modulus without agglomerated and effective matrix phases and they are calculated separately using the Mori-Tanaka homogenization scheme. The capabilities of the modified C-VBO model for nanocomposites are investigated by simulating rate-dependent uniaxial compression, creep, and relaxation behaviors for different graphene fractions (0.1 and 0.5 wt.%). In addition, to investigate high strain rate behavior, Split Hopkinson pressure bar tests are performed. The adiabatic heating effect that occurs at high strain rates is taken into account and incorporated into the model. All behaviors mentioned above are simulated well by simplified C-VBO for nanocomposites. The developed constitutive model is ready to implement into finite element codes to be used in the structural analysis.