Experimental mechanical properties, nonlinear bending and instability analysis of 3D-printed auxetic tubular metastructures using multiscale finite element and Ritz methods
Fatemeh Ghasemi, Erfan Salari, Amir Hosein Zamanian, Abbas Rastgoo
Abstract
In the field of medical technology, specialized equipment utilizes tubular metastructures with a negative Poisson’s ratio in vascular stents to reduce the risk of embolism. The deliberate incorporation of auxetic structures into stent design offers several benefits over traditional stents. This study examines the nonlinear instability and bending responses of reentrant perfect and imperfect 3D-printed tubular metastructures. First, the governing equations for the auxetic tube with geometric imperfections under transverse and axial mechanical loads are derived using the von-Kármán nonlinear assumption and Timoshenko theory. Then, the equations are derived using the principle of virtual displacement. The physical characteristics of the reentrant structure are derived using Malek-Gibson relations, while tensile tests with digital image correlation (DIC) are used to determine the physical properties of polylactic acid (PLA). Scanning electron microscopy (SEM) images help investigate variations in modulus of elasticity and ultimate tensile strength in dogbone specimens, and the Ritz method with Chebyshev polynomials is employed to discretize the nonlinear equations. Second, two numerical algorithms are used to analyze the static behavior of the metatube within the nonlinear framework. The validation study is conducted for the auxetic tube and the representative volume element (RVE) of the unit cell based on the literature and finite element software Abaqus. Following the validation of the mathematical model, an extensive investigation is conducted to assess how differing parameters impact the mechanical bending and nonlinear instability analysis of the reentrant tube.