With a classical notched configuration, the damage process in the transverse plane of fiber-reinforced polymer composites are studied by a direct numerical simulation model (DNS). However, to avoid high computational costs the region in which the fiber/matrix microstructure is explicitly modeled must remain small. Therefore, away from the notch tip, a homogenized model is needed to capture the far-field mechanical response without damage but with possibly rate-dependent nonlinearity. In this contribution, with a representative volume element (RVE), a step-by-step numerical homogenization procedure is introduced to calibrate a homogenized viscoelastic-viscoplastic (VE-VP) model with the same formulation as the VE-VP model used for describing the polymer behavior in the RVE model. The calibrated VE-VP model is used in a homogenized FEM model to describe the composite material response and compared against the RVE model. It is found that: (1) the homogenized model captures the viscoelastic deformation, the rate-dependent yielding, stress relaxation and unloading behavior of the polymer composite well, although the assumptions of a single plastic Poisson's ratio and pure isotropic hardening are oversimplifications of the composite behavior; (2) the novel step-by-step numerical homogenization procedure provides an efficient and accurate way for obtaining material parameters of a VE-VP model.

The deformation-to-fracture evolution of a flexible polymer material under high-strain-rate compressive loading conducted by a split Hopkinson pressure bar (SHPB) setup was investigated. Representative tests were carried out at different strain rate levels, followed by the characterization of dynamic damage after each test. Craze and crack patterns on the end surface of the specimen were carefully analyzed. The failure patterns appear along the radial and circumferential directions. The sequence of their formation with increasing strain/stress level was revealed. The mechanisms resulting in the craze and crack patterns were analyzed. The heterogeneous stress distribution in the specimen and the resultant damage morphologies were demonstrated. This research not only shows the deformation-to-fracture evolution of a flexible polymer material under SHPB loading, but also provides a better clarification of the localized stress distribution in the tested material via SHPB technique.