Analytical and numerical solution and multi-objective optimization of tetra-star-chiral auxetic stents

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Abstract
The present study examines the mechanical properties of auxetic stents with the tetra-star-chiral structure. The tetra-star-chiral geometry is parametrically modeled. Then, the design of experiments (DOE) is developed by defining the elastic properties of the stents and using the response surface method (RSM). Finite element (FE) analysis is performed in order to find a polynomial relationship between the geometric parameters as inputs and the elastic parameters as the outputs. Then, the optimal stent is found in terms of elasticity parameters by using RSM and NSGA-II methods and the two-dimensional Pareto front is plotted. The optimal parameters of the stent including flexural stiffness, axial elasticity modulus, radial elasticity modulus and Poisson’s ratio are obtained as 10.66 mPa m4, 5.37 MPa, 33.2 MPa and − 0.41, respectively. Moreover, a method is proposed to find an analytical solution for metal elastic stents in order to verify the FE model results, and also the blood vessel compliance of the optimal stent is examined.

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