On the hysteretic properties of debonding nanostructured materials

A new paradigm for vibrational energy dissipation can be devised exploiting nanostructured materials made of carbon nanotubes (CNTs). The high interfacial area of CNTs together with the poor bonding properties (when immersed in a polymeric or epoxy matrix) enhances interfacial slippage thus providing high levels of nano/micro-structural hysteresis under cyclic loadings. We present a theoretical and computational framework, based on the Eshelby-Mori-Tanaka approach (e.g., see [1]), for the elastodynamic response of CNT-based composites. The description of hysteresis is achieved within a thermodynamically consistent constitutive characterization that stems from the definition of an effective micromechanically-derived yield criterion. Such criterion is based on the models developed by Ju et al. (e.g., see [2]) and Zhou et al. (e.g., see [3]). In particular, the constitutive laws here proposed describe the composite as a three-phase material which gradually evolves. The three phases refer to perfectly bonded fibers, partially/completely debonded fibers, and to the elastic hosting matrix, respectively. The evolving laws obey to the Weibull statistics, in terms of average interfacial strength and debonding rate (e.g., see [4]). The present approach aims to improve the knowledge of the vibrational characterization of CNT composites, previously described within the context of equivalent linear elasticity with perfect bonding [5], and it provides a first-order analytical foundation for the estimation of the effective damping properties and optimal tuning of the dissipation parameters for different applications, as the numerical testing campaigns illustrate.