The objective of this project was to understand, design, and evaluate composite materials containing engineered microstructures that display negative stiffness (NS) and negative Poisson s ratio (auxetic) behavior. The ultimate aim for understanding such microstructural elements is to enable the creation of composite materials that are significantly more dissipative than currently available materials to enhance existing mechanical absorption and isolation capabilities without degrading stiffness performance. Progress has been made in the design and analysis of NS microstructures that exploit buckled element geometry to produce NS behavior. The nonlinear effective material properties of the microstructure have been obtained using finite element analysis and the overall behavior of a composite material containing NS inclusions has been determined using combined FEA and analytical effective medium theory. Auxetic materials work has produced particulate composite materials containing auxetic ?-crystobalite inclusions. The resulting composite materials have been characterized using quasistatic, modal vibration, and ultrasonic methods together with extensive microscopy. The knowledge gained during the work of this project can be used in future research to provide a basis for the design of microstructures that can aid in absorbing vibroacoustic energy to improve overall composite material performance through variations of engineered microstructure.