Materials and Methods for implementing engineered aggregates in metamaterials are provided. The engineered aggregates may be tuned to oscillate resonantly under the influence of an external force improving the dynamic performance of the metamaterial by impeding dynamic excitation. The engineered aggregate generally comprise a multilayer resonant structure having at least a relatively heavy inner core surrounded by at least a compliant coating layer. The geometry and stiffness of the relative layers can be tuned to engineer a desired resonant frequency response within the aggregate for a chosen frequency range. The engineered aggregates are disposed in a matrix material to form a metamaterial. The engineered aggregates may be disposed within a mortar matrix to form a concrete metamaterial suitable for use, for example, in structural applications, including bunkers, shelters, etc.