Multiscale Mass-Spring Models of Carbon Nanotube Arrays Accounting for Mullins-like Behavior and Permanent Deformation

Abstract

Abstract. Based on a one-dimensional discrete system of bistable springs, a mechanical model is introduced to describe plasticity and damage in carbon nanotube (CNT) arrays. The energetics of the mechanical system are investigated analytically, the stress-strain law is derived, and the mechanical dissipation is computed, both for the discrete case as well as for the continuum limit. An information-passing approach is developed that permits the investigation of macroscopic portions of the material. As an application, the simulation of a cyclic compression experiment on real CNT foam is performed, considering both the material response during the primary loading path from the virgin state and the damaged response after preconditioning.

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

“…Mechanical properties of the single spring models in figure 6 (k 0 = k 0 /ρ (MPa cm 3 g −1 )). plastic' behavior at the microscopic scale (transformational plasticity), it is worth noting that the multiscale grading of material properties leads to hardening of the overall (macroscopic) stress-strain response [26][27][28].…”

“…(2) We discuss the physical anisotropy of the material and how it affects the mechanical response of the system (showing the importance of taking the loading direction into account when designing materials based on CNT arrays for optimal performance in applications such as protective foams). (3) We discuss the experimental observations above in the context of a one-dimensional model based on bistable elements in series that we developed previously [26][27][28]. The model is able to capture the global stress-strain response of CNT arrays as well as the local deformation that is observed in such systems.…”

Multiscale Mass-Spring Model for High-Rate Compression of Vertically Aligned Carbon Nanotube Foams

“…Eventually, the overall response of a CNT structure can be described through a single dissipative element (macroscopic mass-spring model [10,25]). This multiscale model has been previously applied to describe the quasi-static response of CNT structures [10,19,20,21,25]. Here, the same model is applied to describe the mechanical response of VACNT foams under high-rate loading in association with the phenomenological damping devices [22].…”

“…This model does not allow for accumulation of permanent strains that is often found in the compression experiments of VACNT foams, both in their quasi-static [1] and dynamic [7] responses. However, it can be modified to prevent snap-back recovery of springs and allow permanent damage [21]. Similarly, the model can be generalized to describe preconditioning effects found in cyclic loading, by introducing initial strains, e i 0 !…”

“…This model also enabled in situ material parameter identification in multilayered CNT arrays, and allows modeling experimentally observed local deformations accurately [20]. It has been extended later to describe a few experimentally observed phenomena, such as preconditioning [20], loading history, and loading direction dependency [10] and permanent damage [21]. However, numerical models of high-rate, uniaxial, finite deformation of VACNT foams have not yet been developed.…”