Cellular solids are ubiquitous in many engineering applications, ranging from automotive to aerospace and sport protective gears, offering superior impact mitigation in various dynamic loading conditions. Some desirable mechanical attributes of cellular solids include enhanced energy absorption, strength, and stiffness at low weight penalty to the overall structure. The latter is essential in dynamic loading conditions to minimize the inertial effects of catastrophic material and structural failures. While stochastic cellular solids (i.e., foams) have been vigorously investigated, their ordered counterparts only recently grabbed scientific and technological attention since additive manufacturing technologies readily enabled the realization of such intricate and complex structures. This research aims to assess the mechanical performance of ordered cellular solids, also known as lattice structures, fabricated from a wide range of polymers and various geometrical configurations. The approach hinges on constructing finite element simulations capable of capturing the mechanical behavior of the base polymers using nonlinear mechanical models. Several lattice structures are generated based on triply periodic minimal surfaces and translated into the finite element solver, where quasi-static and dynamic mechanical loading are strategically applied to extract the global stress-strain behavior and concurrently probe the local deformation mechanisms. The global stress-strain responses are then used to assess the efficacy of these tailored structures as a function of the loading scenario, e.g., loading rate, by calculating the specific energy absorption and efficiency. The probed deformation mechanisms are cataloged and associated with key performance metrics commonly used for selecting microcellular geometries in real-life engineering applications. The major outcome of this preliminary virtual experimentation is identifying the most promising microcellular topology for 3D printing and physical characterization. The results of this research will be used to develop optimal protective gear to eliminate or substantially mitigate traumatic brain injuries in action sports such as football.