A novel methodology is presented to introduce Periodic Boundary Conditions (PBC) on periodic Representative Volume Elements (RVE) in Finite Element (FE) solvers based on dynamic explicit time integration. This implementation aims at overcoming the difficulties of the explicit FE method in dealing with standard PBC. The proposed approach is based on the implementation of a user-defined element, named a Periodic Boundary Condition Element (PBCE), that enforces the periodicity between periodic nodes through a spring-mass-dashpot system. The methodology is demonstrated in the multiscale simulation of composite materials. Two showcases are presented: one at the scale of computational micromechanics, and another one at the level of computational mesomechanics. The first case demonstrates that the proposed PBCE allows the homogenization of composite ply properties through the explicit FE method with increased efficiency and similar reliability with respect to the equivalent implicit simulations with traditional PBC. The second case demonstrates that the PBCE coupled with Periodic Laminate Elements (PLE) can effectively be applied to the computational homogenization of elastic and strength properties of entire laminates taking into account highly nonlinear effects. Both cases motivate the application of the methodology in multiscale virtual testing in support of the building-block certification of composite materials.