In this study, damage evolution in a nanocomposite containing the polymethyl methacrylate polymer (PMMA) embedded with silicate nanoclay particles is simulated by using a nonlinear viscoelastic, viscoplastic, and viscodamage constitutive model. Mesomechanical two-dimensional representative volume elements (RVEs) of fully intercalated and fully exfoliated nanoclay polymer composites have been arbitrarily generated assuming a uniform dispersion of nanoclay particles with random length, aspect ratio, and orientation. Proper size of the RVE has been determined by studying the effect of the RVE size on the stress-strain response and toughness. Several simulations including different intercalated and exfoliated nanoclay weight fractions under different strain rates at room temperature have been conducted. It is concluded that the strength of exfoliated nanoclay composite is higher than intercalated one due to more distributed damage within many narrow localized zones for the case of exfoliated nanoclay polymer composite.