A composite material includes a metallic second phase dispersed in a metallic matrix material. The metallic second phase has a grain structure that is at least partially martensitic. The second phase material is preferably an alloy of nickel and titanium, each present in the range from 48 to 52 atomic %, optionally in combination with further additives. The second phase particles can be present in the form of granular particles, wires, fibers, whiskers, or layers, making up 5 to 60 vol. % of the overall composite material. The matrix material is preferably an aluminum alloy. The composite material has a high damping capacity and a high tensile strength provided by the matrix, and a high damping capacity provided by the second phase. A method of making the composite material involves mixing a powdery matrix material and a powdery second phase material, and then heat and consolidating the mixture at a temperature of 400 to 700 ° C. and a pressure of 100 to 300 MPa.