The Postbuckling Behavior of Compressed Elastica Inside a Flexible Tube: Experimental and Numerical Investigation

The post-buckling behavior of an elastic fiber subjected to lateral constraints is of practical importance in a wide range of medical and engineering applications. The vast majority of existing studies have adopted the assumption that the lateral constrains are fixed in space and rigid. This assumption is often far from the reality of the physical complexity of the abovementioned systems. In this paper, we study analytically, numerically, and experimentally, the behavior of an elastic fiber that is subjected to compressive force and constrained by a flexible tube. The latter marks a point of departure from available research. Our experiments provide quantitative information related to the overall behavior of the system, like force-shortening relation and deflection of the flexible tube. That information is complemented by finite-element simulations that enable in-depth analysis of the deformation of the fiber as well as contact characteristics between the fiber and the inner wall of the flexible tube. Finally, a simple mathematical model, aimed at providing analytical insights, is presented. Overall, the theoretical, numerical, and experimental results are in very good agreement. They highlight the fact that the behavior of a compressed fiber that is constrained by a deformable tube significantly deviates from that of a fiber constrained inside a rigid cylinder. Moreover, it is shown that the overall behavior as well as the evolution of contact between the fiber and the cylinder heavily depend on the ratio between the stiffness of the fiber and the lateral stiffness of the tube.

Nonlinear Postbuckling of Auxetic-Core Sandwich Toroidal Shell Segments with CNT-Reinforced Face Sheets Under External Pressure

Nonlinear buckling analysis for honeycomb auxetic-core sandwich toroidal shell segments with CNT-reinforced face sheets surrounded by elastic foundations under the radial pressure is presented in this study. The basic equation system of shells is established based on the von Kármán–Donnell nonlinear shell theory, combined with Stein and McElman approximation. Meanwhile, the foundation-shell elastic interaction is simulated by the foundation model based on the Pasternak assumption. The Galerkin procedure is utilized to achieve the pre-buckling and post-buckling responses for the shell, from which the radially critical buckling load is determined. Numerical analysis shows the various influences of auxetic-core layer, CNT-reinforced face sheets, and elastic foundation on the pre-buckling and postbuckling behavior of sandwich shells with CNT reinforced face sheets.

An analytical approach to the nonlinear buckling behavior of axially compressed auxetic-core cylindrical shells with carbon nanotube-reinforced coatings

Auxetic materials are usually designed as cores for structures subject to high impulse loads. Furthermore, the lightweight and high load capacity of the auxetic core construction is also an important advantage even for structures subjected to static loads. The combination of auxetic core and face sheets made by the advanced composite materials is a solution to dramatically increase the load-carrying capacity of the structure. In this paper, a new design of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings is presented. Additionally, the nonlinear buckling behaviors of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings under axially compressive loads are investigated. Three distributed types of functionally graded carbon nanotube-reinforced coatings and the honeycomb lattice form of the auxetic core are investigated. The homogenization model for auxetic lattice structures is considered to constitute the formulations of stiffnesses of the core layer. The nonlinear basic formulations are formulated by using the geometrically nonlinear Donnell shell theory considering Pasternak’s foundation. The Galerkin procedure can be applied three times for three states of buckling behaviors, and the expressions of the compressive load-maximal deflection and compressive load-average end shortening postbuckling curves are achieved. The numerically obtained investigations present the significant effects of auxetic core, volume fraction, direction arrangement and distributed law of carbon nanotube, foundation stiffnesses, geometrical parameters of auxetic core and shell on the critical buckling load and postbuckling behavior of structures.