In this work, we extend the variational multiscale enrichment (VME) method [1] to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under scale-inseparable conditions, including short-wavelength regimes, while accounting for material and geometric nonlinearities that lead to wave steepening or flattening. By employing an additive decomposition of the displacement field, we derive multiscale governing equations for the coarse- and fine-scale problems, which naturally incorporate micro-inertial effects. An operator-split procedure is used to iteratively solve the semi-discrete equations at both scales until convergence is achieved. The coarse-scale problem is integrated explicitly, while the fine-scale problem is solved using either explicit or implicit time integration schemes, including both dissipative and non-dissipative methods. One-dimensional numerical examples demonstrate that dissipative schemes [2] outperform non-dissipative methods, such as the explicit central difference method, by effectively suppressing spurious oscillations, which are present even in homogeneous media. The multiscale framework is further applied to investigate how material and geometric nonlinearities, along with elastic stiffness contrast in heterogeneous microstructures, influence key wave characteristics such as dispersion, attenuation, and steepening. The VME results show close agreement with direct numerical simulations, validating the method’s accuracy and robustness. This framework provides a foundation for developing reduced-order multiscale models of dynamic response in architected materials, where the fine-scale problem can be efficiently approximated using data-driven surrogate models. References: [1] Hu, R. and Oskay, C., 2020. Spectral variational multiscale model for transient dynamics of phononic crystals and acoustic metamaterials. Computer Methods in Applied Mechanics and Engineering, 359, p.112761. [2] Noh, G. and Bathe, K.J., 2013. An explicit time integration scheme for the analysis of wave propagation. Computers & Structures, 129, pp.178-193.