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Wave propagation in granular media composed of contacting discrete elastic granules attracted considerable attention due to its highly tunable acoustic properties. While prior investigations focused on granular systems with natural boundaries (e.g., fixed or free), our study delves into two-dimensional nonlinear wave propagation within hybrid metamaterials composed of ordered granular media interacting with linearly elastic solids, employing discrete element modeling for the granular media and finite element analysis for the elastic solids. Challenges resulting from numerical instabilities arise from non-smooth contact nonlinearities and friction at granular and granular–solid interfaces. To tackle the numerical challenges, we developed an interrelated interpolation-iteration algorithm with a self-adaptive time scheme. Special consideration was given to the convergence of contact forces at the granular–solid interface. Specifically, to ensure robust computational modeling without numerical instabilities, we monitored the eigenvalues of appropriately defined local maps governing the iterative computations of the contact forces. We demonstrated the capacity of these hybrid metamaterials for shock mitigation and non-reciprocal acoustics with properties that are passively tuned (self-adaptive with) energy. Such results and computational methods contribute to the predictive modelling and design of 2D granular media with flexible interfaces, with diverse applications, e.g., in shock protectors and acoustic diodes.
Wang et al. (Fri,) studied this question.