Multistage Modeling And Mechanical Properties Of Superconducting Cables Based On Discrete Element Method

Superconducting cables,which normally consist of thousands of strands twisted through multiple stages,are a key part of the magnet system of the International Thermonuclear Experimental Reactor(ITER).Although the strand itself is continuous,the interactions between adjacent strands exhibit distinct discreteness and involves complex multi-body contact characteristics.Because the superconducting cables are usually used in environments with a strong magnetic field,large current,and extremely low temperature,they will experience local deformation and non-uniform contact of their interior strands,resulting in the degradation of its superconducting performance.As a result,it is crucial to establish the theoretical models that can describe the macroscopic deformation characteristics of cables at various stages,and use them to predict and analyze the mechanical behavior at different scales within the cable,which is critical for improving the operating stability of the magnet system and optimizing its structural design.This academic dissertation presents a novel bottom-up methodology for establishing three-dimensional models of multi-stage superconducting cables based on the discrete element method,with the goal of addressing the discreteness and multiscale properties of superconducting cables.According to several stages of superconducting cables with diverse components and architectures,a multi-stage discrete element model incorporating the twisting effect of strands is developed by introducing an effective contact force law between elements with different functions and materials.On this basis,the mechanical behaviors such as localized deformation and non-uniform contact at the scale of the sub-cables up to the strand scale under complex external forces and different operating conditions are systematically studied.The main work of the dissertation is as follows:1.Selecting an appropriate contact force model to accurately characterize the contact deformation characteristics between different functional and material units is a key issue when using the discrete element method to model superconducting cables with spatial helical structures and complex components.In this study,we review the most commonly used contact models in the discrete element method,as well as the advantages,drwabacks,and applicability of related models for modeling the contact deformation between spheres.An improved elastic-plastic contact model is proposed,and a tangential force model coupled is also developed,baded on the collision process and contact deformation characteristics of spheres.Furtheromore,the outcomes of the normal and oblique collisions between spheres can be used to not only verify this improved model,but also to help determine some model parameters.The corresponding discrete dynamic model and numerical calculation method are developed based on the aforesaid model,and the feasibility and effectiveness of the calculation model in discrete media involving large-scale discrete element calculations are also discussed.2.A new bottom-up methodology for constructing a 3D model of multi-stage superconducting cable is proposed based on the discrete element method.Considering the shape and structural properties of superconducting strand,a DEM model that can characterize the geometry and deformation characteristics of a single strand is constructed by using the discretization method of the continuum and introducing improved cohesive bond between discrete spheres in the strand,and the microscopic parameters of the cohesive bond are calibrated.Furthermore,the spatially geometric configuration of multistage cable is generated on the basis of the cylindrical spiral equations of different twisted stages,and by introducing the law of contact force between spheres to characterize the interaction between strands in cables,DEM models of cables at different stages are constructed step by step.Aiming at the initial model of high-stage cable,the way of cable compaction and the method of eliminating internal pre-stress was given.An elastic-plastic contact force law is introduced into the model to characterize the plastic deformation effect caused by the contact between strands,which solves the problem of deviation between the prediction results and experimental results of the third stage cable model under high transverse stress level.3.Based on the proposed multi-stage modeling method of superconducting cable,discrete element models of multi-stage cables with different twist pitch are established in this paper.For the first and second cable,we predicted the influence of twist pitch on cable axial deformation characteristics,equivalent Young's modulus,the axial strain distribution and the influence of contact characteristics between the strands,and compared them with the theoretical model of elastic deformation stage based on thin rod theory so as to discuss the limitation of the theoretical model.For the third stage cable,the influence of twist pitches of different stage on the mechanical behaviors of the cable under axial tension were studied,the dependence of the overall deformation of the cable on the local deformation characteristics of the sub-cables and strands in the cable,and the effect of twist pitches of different stage on these dependence relationships were discussed.4.The macroscopic deformation characteristics of cable under transverse cyclic compression are systematically examined based on four DEM models for different third-stage cables.We investigated the variation characteristics of cable's transverse plastic deformation,equivalent elastic modulus and mechanical loss with the number of loading cycles using the obtained load-displacement curve.This research also shows how the arrangement structure,deformation distribution,and contact characteristics of the strands inside the cable evolve with the number of cyclic loading cycles.The influence of twist pitch and void fraction on the transverse displacement and contact characteristics of strand in cable is investigated,as well as main factors affecting the macroscopic mechanical behavior and structural stability of the cable.5.Based on the bottom-up multi-stage modeling approach,we established a discrete element model containing STP and CWS superconducting cable with Cu strands by bringing in the contact constitutive equation describing deformation characteristics of materials of different components.Aiming at different winding directions of copper strands in CWS cable,the three-dimensional geometric equation describing their structure is given,and the corresponding compaction forming method is developed.For the deformation of first stage cable under axial tension,the effect of Cu strand ratio and pitch on equivalent tensile stiffness and the contact characteristics of the between the strands in cable is studied here.The way to express thermal strain and Lorentz force in DEM model is given and,what's more,an equivalent method for calculating axial local strain of strand in discrete element model is developed by considering bending strain.On this basis,we studied the local deformation characteristics of third stage cable under thermal strain and Lorentz force,and discussed the influence of Cu strand as well as its winding direction on the stability of the superconducting cable.This dissertation proposes a new bottom-up methodology for constructing a threedimensional numerical model of multi-stage superconducting cable,foucs on superconducting cable with typical discreteness and multiscale properties.It has been confirmed that the DEM model based on this method is capable of accurately describing the macroscopic deformation features of cable at various stages under external force.Furthermore,it can be used to quantitativly predict of mechanical behavior within the cable from subcable down to strand.The research presented in this dissertation provides a theoretical foundation and microscopic mechanism for revealing and analyzing macroscopic mechanical behavior of superconducting cables of different stages under the action of complex external forces,as well as a proven theoretical modeling strategy and quantitative analysis method for the investigation of problems involving complex multi-scale structure with discrete properties similar to superconducting cables.