The Mechanical Analysis Of Superelastic Helical Structure

With the development of investigations about crystalline phases discipline of super-elastic shape memory alloys(SMAs)in microscopic levels,the shape memory effect(SME)and super-elasticity are able to be explained completely,which obviously drove the design and application of SMAs in macroscopic levels in recent years.The unique helical structure makes significant contributions to numerous outstanding characters of helical springs,such as the prominent resistance of shock absorber,favorable flexibility and excellent designability.The helical spring can obtain admirable comprehensive functions,such as the resistance of deformation,fatigue strength and dynamic response,by means of reasonable options of the parameters of materials and geometry.Because of the successful integration of various advantages of the SMAs and helical structures,springs made of super-elastic SMAs are widely applied and win general consent in engineering community.Many scholars have studied the super-elastic helical structures in terms of the establishment of analytical models,finite element analysis and experiments.The finite element method,an approximate numerical method based on the theory of discrete mathematics,is widely used in engineering.Although the results are approximate,they are enough for project application.As for experiments,although it is tough to design and set up a practical experimental platform,investigators can exert real boundary conditions and loads to obtain visualized phenomena.These two methods become main tools to study helical structures made of SMAs.Compared with finite element methods and experiments,analytical models is apparently insufficient,on account of their limitations on describing unusual deformations of super-elastic helical springs under complex conditions.However,completed analytical models is indispensable and accurate for deformations under common operating conditions,which is helpful for improving design efficiency and shortening design cycles.Based on previous analytical model describing free extension of helical structures and simplified constitutive model of SMAs,this paper provide a theoretical model to establish the relationship between radial compression under uniform radial pressure and free extension,and finally get the relationship between the pressure and radius of coils.Finite element models are used to prove it effective and precise.Furthermore,this theoretical model is generalized to the application of braided stents for interventional therapy and both applicability and error analysis is discussed in this paper.Besides,the quasi-theoretical model is presented to describe another deformation form is taken into consideration,when a helical braided stents is stretched along axial direction with ends fixed in radial direction.Firstly,equations of the envelope surface encompassing deformed braided stents is fitted by the results of finite element methods.Then the equation of deformed helix in the envelope surface is constructed,which is the analytical origin of curvature and twist of each point on the curve.The bending moment and torque on arbitrary cross section can be obtained via integration based on the constitutive relation of SMAs.Finally,equilibrium equations between external loads and internal force is established,which is able to depict the relationship between deformations of braided stents and axial stretch force.Numerical analysis is applied to support the applicability and accuracy this theoretical model.This model can not only commendably explain the operating principle of cable grips produced by CABLE GRIP but also provide effective assist in design process.