Tensile and thermo‐mechanical properties of nano‐composites fabricated by mechanically mixing semi‐crystalline ethylene‐co‐butyl acrylate (EBA) and carbon black (CB) nanoparticles are investigated. Stress–strain curves performed on samples over a broad range of CB content evidence the hyperelastic behavior of the EBA matrix. Neo‐Hookean and Mooney‐Rivlin models are used to fit the observed linear and nonlinear mechanical behaviors, respectively. The thermo‐mechanical curves highlight two relaxation phenomena depending on the CB content. Correspondingly, the EBA/CB interface properties are analyzed by correlating the volume fraction of the constrained polymer to the relaxation behavior of the viscoelastic linear regime. POLYM. COMPOS., 40:3005–3011, 2019. © 2018 Society of Plastics Engineers