This paper proposes a physically sound elasto-plastic damage constitutive model, through following Mohr's fracture hypothesis, to characterize pressure sensitivity, nonlinear behaviors and isotropic damage of epoxy matrix materials. Upon the consideration with geometric non-uniformities and mechanical behaviors of constituents, a micromechanical analysis is carried out to study failure mechanisms within fiber-reinforced polymer composite materials applied by different loading scenarios. In particular, special focus is given to the values and distributions of fracture plane angles on multi-scales - the fiber scale and the lamina scale, and therefore both damage scenarios and dominant failure mechanisms are further revealed. The influence of shear nonlinearity of epoxy matrix on overall composite shear responses is assessed from a parametrical study, showing that the composite response induced by longitudinal shear is more susceptible the matrix shear property, when comparing with transverse shear. At last, another use of the proposed micromechanical model is presented. With the use of strength properties and fracture angles captured by micromechanics, the parameters (R⊥At, p⊥⊥t and p⊥⊥c) in Puck's criterion can be computed without making any assumption sometimes arguable. In general, the numerical results regarding homogenized stress-strain responses as well as fracture morphology agree well with experimental measurements and theoretical analyses, validating the predictive capacity of the proposed model.