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Analysis of mechanical behavior on anisotropic cylindrical superconducting materials with inclusions

含夹杂各向异性圆柱超导材料的力学行为分析

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Abstract

This paper presents a theoretical and numerical analysis of the magnetoelasticity of a long cylindrical superconductor model containing a central inclusion placed in a time-dependent external magnetic field with zero-field-cooled magnetization (ZFC). In order to reflect the mechanical behavior of the model more realistically, the model is defined as a material with anisotropic mechanical properties, and then the viscous flux flow effect and the flux creep effect are considered separately for the flux distribution of the model. By controlling the elastic modulus E ir /E mr , volume fraction f of composite materials, as well as the parameters affecting the flux distribution, such as the viscous flux flow velocity v1, the flux creep action coefficient K, the creep occurrence probability n, etc., the radial stress distribution and magnetostriction characteristics of the model are analyzed in depth. In this paper, the theoretical calculation results are compared with the numerical simulation results. The results show that the distribution laws of the parametric curves plotted by the two are almost completely consistent, but there are obvious differences in the numerical values. The reason is that the superconductor conductivity is assumed to satisfy a strong nonlinear E-J relationship in the numerical simulation process, and an external magnetic field in the form of a pulse is applied; while the field-dependent critical state model is used in the theoretical calculation, and the induced current is assumed to be a critical current, so there are certain differences in the calculated values.

摘要

本文对零场冷却充磁(ZFC)后放置于随时间变化的外磁场中的含中心夹杂长圆柱超导体模型磁弹性问题进行解析计算和数值计算分析. 为了更加真实地反映模型的力学行为, 首先将模型定义为磁性能各向异性材料, 其次对模型的磁通分布状态分别考虑了外场黏性磁通流动效应和内场磁通蠕变效应. 通过控制复合材料的弹性模量E ir /E mr 、体积分数f 等弹性系数以及影响磁通分布的黏性磁通流动速度v1 、磁通蠕变作用系数K、蠕变发生几率n等参变量的取值, 对模型的径向应力分布状态和磁致伸缩特性进行深入分析.将本文的解析计算结果与数值模拟结果进行了比较, 结果反映两者绘制的参变量曲线分布规律几乎完全吻合, 不同的是数值大小存在明显差异, 其原因为数值模拟过程中假定超导体电导率满足强非线性E-J关系, 并施加了脉冲形式的外磁场; 而解析计算过程中采用了场相关的临界态模型, 将感应电流假定为临界电流, 所以导致计算结果数值存在一定差异.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51904138 and 51076061), and the Natural Science Foundation of Gansu Province (Grant No. B061709). The authors are also grateful to the anonymous reviewers for their constructive comments.

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Authors and Affiliations

  1. Key Laboratory of Mechanics on Environment and Disaster in Western China, Ministry of Educatio, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000, China

    Wenhai Zhou  (周文海) & Youhe Zhou  (周又和)

  2. School of Petrochemical Technology, Lanzhou University of Technology, Lanzhou, 730050, China

    Wenhai Zhou  (周文海)

Authors
  1. Wenhai Zhou  (周文海)
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  2. Youhe Zhou  (周又和)
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Correspondence to Wenhai Zhou  (周文海) or Youhe Zhou  (周又和).

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Author contributions

Zhou Youhe designed the study and put forward the overall research objectives, methods and research ideas. Zhou Wenhai modeled the research content, analyzed the data and detailed writing process to form the first draft. On this basis, the first draft was reviewed and revised, and put forward constructive suggestions. In the end, Zhou Wenhai revised the article several times according to Zhou Youhe’s opinions and formed the final draft.

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Zhou, W., Zhou, Y. Analysis of mechanical behavior on anisotropic cylindrical superconducting materials with inclusions. Acta Mech. Sin. 39, 122168 (2023). https://doi.org/10.1007/s10409-022-22168-x

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