Shape memory alloys (SMA) have long been explored as a semi-passive approach to mechanical energy dissipation particularly, but not exclusively, for application to vibration control. More recently, the integration of SMAs in composite materials has opened the opportunity to synthesize tunable composite structures exhibiting significantly enhanced energy dissipation characteristics and a certain degree of adaptability to different operating conditions. Despite the significant progress in the development and manufacturing of SMAs over the past several decades, the cost of common Ni-based alloys has remained an important factor hindering their widespread engineering application. The long-term goal of this research effort is to model, design, and fabricate shape-memory-alloy (SMA) meta-composites employing lower volume fractions of a more affordable Cu-based alloy, while still enabling enhanced and tunable dynamic properties. This paper summarizes recent progress in the development of the meta-composite platform and focuses on aspects involving both numerical modeling and fabrication of SMA materials. On the modeling side, particular emphasis is given to assess the ability to tune the dynamic performance of continuous SMA structures by exploiting the different phases and transformations of the alloy. On the other side, the material development effort focuses on the identification of the optimal chemical composition, mechanical and heat treatment processes. A combination of numerical and experimental results is presented to illustrate capabilities and opportunities presented by this material platform.