Composites are multiphasic materials with individual constituent parts that work cooperatively to produce some desired result. For the common case of structural composites, the use of nanoscale additives does not always yield a predictable outcome due to the complex interactions that occur in the interfacial region where a reinforcing filler meets the supporting matrix. It stands to reason, however, that the thoughtful and deliberate exploitation of unusual effects in this region could lead to the development of nanocomposite materials with extraordinary properties. In this thesis work, I will introduce two such responses in a compliant nanocomposite consisting of highly-aligned carbon nanotubes (CNTs) encased within a poly(dimethylsiloxane) (PDMS) matrix. It is first demonstrated that the material exhibits extremely anisotropic dynamic mechanical behavior. The composite will behave in a way that is evocative of the neat polymer when deformed orthogonal to the CNT alignment direction, yet will exhibit strain softening when cyclically compressed along their axis due to the collective buckling of the nanotube struts. Next, it is shown that this nanocomposite material has the ability to respond and adapt to applied loads. Independent, yet complimentary tests reveal that the structure of the polymer in the presence of nanoscale interstitials will evolve during dynamic stressing, an effect that was predicted nearly 50 years ago. With support from both recent and established literature, an updated mechanism is proposed. Collectively, these results provide insight into the complicated mechanics between polymer matrices and embedded nanoparticles, and assist in the design of advanced synthetic materials with unique physical properties.