Micromechanics simulations of fiber-reinforced polymer-matrix composites with waviness defects are conducted to investigate the effect of constitutive model selection on the nucleation, evolution, and interaction of damage modes under in-plane compression. A 2D finite element model with fibers, matrix and fiber-matrix interfaces is used, considering damage modes at the constituent level (i.e., fiber-matrix interface damage, matrix plasticity, void nucleation and growth). Results show that the pressure-dependency of the polymer matrix is key for accurate predictions of strain localization in the fiber kinking mode and fiber-matrix interface crack behavior and extent at regions of waviness imperfections.