Multiscale mass-spring models of carbon nanotube foams

• Published in: Journal of the mechanics and physics of solids 2011, Vol.59 (1), p.89-102
• Main Authors: Fraternali, F., Blesgen, T., Amendola, A., Daraio, C.
• Format: Article
• Language: English
• Subjects: Bi-stable springs; Carbon nanotube foams; Chains; Compressive properties; Dissipation; Foams; Hysteresis; Mathematical analysis; Mathematical models; Multiscale behavior; Springs; Springs (elastic); Strain localization
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2010.09.004

This article is concerned with the mechanical properties of dense, vertically aligned CNT foams subject to one-dimensional compressive loading. We develop a discrete model directly inspired by the micromechanical response reported experimentally for CNT foams, where infinitesimal portions of the tubes are represented by collections of uniform bi-stable springs. Under cyclic loading, the given model predicts an initial elastic deformation, a non-homogeneous buckling regime, and a densification response, accompanied by a hysteretic unloading path. We compute the dynamic dissipation of such a model through an analytic approach. The continuum limit of the microscopic spring chain defines a mesoscopic dissipative element (micro–meso transition) which represents a finite portion of the foam thickness. An upper-scale model formed by a chain of non-uniform mesoscopic springs is employed to describe the entire CNT foam. A numerical approximation illustrates the main features of the proposed multiscale approach. Available experimental results on the compressive response of CNT foams are fitted with excellent agreement. Axial strain localization in a mesoscopic chain of five bistable springs. The spring collapse mimics the local kinking of compressed carbon nanotubes. Predicted stress-strain response (solid line) at the macroscopic scale, reproducing the experimental behavior of a real CNT foam (dashed line). [Display omitted] ► Axial strain localization in microscopic bi-stable spring chains mimics kinking of compressed carbon nanotube arrays. ► Infinitesimal viscous events at the microscale induce time-independent hysteresis at the mesoscale. ► Multiscale mechanical modeling of CNT foams is obtained through an information-passing approach. ► Available experimental results on compressed CNT foams are reproduced with excellent agreement.