Rate-independent dissipation and loading direction effects in compressed carbon nanotube arrays

Arrays of nominally-aligned carbon nanotubes (CNTs) under compression deform locally via buckling, exhibit a foam-like, dissipative response, and can often recover most of their original height. We synthesize millimeter-scale CNT arrays and report the results of compression experiments at different strain rates, from 10(-4) to 10(-1) s(-1), and for multiple compressive cycles to different strains. We observe that the stress-strain response proceeds independently of the strain rate for all tests, but that it is highly dependent on loading history. Additionally, we examine the effect of loading direction on the mechanical response of the system. The mechanical behavior is modeled using a multiscale series of bistable springs. This model captures the rate independence of the constitutive response, the local deformation, and the history-dependent effects. We develop here a macroscopic formulation of the model to represent a continuum limit of the mesoscale elements developed previously. Utilizing the model and our experimental observations we discuss various possible physical mechanisms contributing to the system's dissipative response.