Numerical methods for the magneto-mechanical coupling analysis of invessel components in Tokamak devices

Magneto-mechanical coupling vibration arises in the in-vessel components of Tokamak devices especially during the plasma disruption. Strong electromagnetic forces cause the structures to vibrate while the motion in turn changes the distribution of the electromagnetic field. To ensure the Tokamak devices operating in a designed state, numerical analysis on the coupling vibration is of great importance. This paper introduces two numerical methods for the magneto-mechanical coupling problems. The coupling term of velocity and magnetic flux density is manipulated in both Eulerian and Lagrangian description, which brings much simplification in numerical implementation. Corresponding numerical codes have been developed and applied to the dynamic simulation of a test module in J-TEXT and the vacuum vessel of HL-2M during plasma disruptions. The results reveal the evident influence of the magnetic stiffness and magnetic damping effects on the vibration behavior of the in-vessel structures. Finally, to deal with the halo current injection problem, a numerical scheme is described and validated which can simulate the distribution of the halo current without complicated manipulations.

A Nonlinear Magneto-Mechanical Coupled Constitutive Model for the Magnetostrictive Material Galfenol

In order to predict the performance of magnetostrictive smart material and pushits applications in engineering, it is necessary to build the constitutive relations for themagnetostrictive material Galfenol. For Galfenol rods under the action of the pre-stress andmagnetic field along the axial direction, the one-dimensional nonlinear magneto-mechanicalcoupling constitutive model is proposed based on the elastic Gibbs free energy, where theTaylor expansion of the elastic Gibbs free energy is made to obtain the polynomial forms. Andthen the constitutive relations are derived by replacing the polynomial forms with the propertranscendental functions based on the microscopic magneto-mechanical coupling mechanism.From the perspective of microscopic mechanism, the nonlinear strain related to magneticdomain rotation results in magnetostrictive strain changing with the pre-stress among theelastic strains induced by the pre-stress. By comparison, the predicted stress-strain,magnetostrictive strain, magnetic induction and magnetization curves agreed well withexperimental results under the different pre-stresses. The proposed model can describe notonly the influences of pre-stress on magnetostrictive strain and magnetization curves, butalso nonlinear magneto-mechanical coupling effect of magnetostrictive materialsystematically, such as the Young’s modulus varying with stress and magnetic field. In theproposed constitutive model, the key material constants are not chosen to obtain a good fitwith the experimental data, but aremeasured directly by experiments, such as the saturationmagnetization, saturation magnetostrictive coefficient, saturation Young’s modulus, linearmagnetic susceptibility and so on. In addition, the forms of the new constitutive relationsare simpler than the existing constitutive models. Therefore, this model could be appliedconveniently in the engineering applications.

Magnetoelastic coupling effect of Fe10Co90 films grown on different flexible substrates

The magneto-mechanical coupling effect and magnetic anisotropy of Fe10Co90(FeCo)films deposited on silicon wafer(Si),flexible polyethylene terephthalate(PET),freestanding polydimethylsiloxane(PDMS),and pre-stretched 20%PDMS substrates were studied in detail.The loop squareness ratio Mr/Ms and the coercive Hc of the FeCo film grown on a PET substrate can be obviously tuned by applying a small tensile-bending strain,and those of the FeCo film grown on a freestanding PDMS substrate can only be slightly changed when applying a relatively large tensile bending strain.For the FeCo film prepared on a 20%pre-stretched PDMS,a wrinkled morphology is obtained after removing the pre-strain.The wrinkled FeCo film can keep the magnetic properties unchanged when applying a relatively large tensile bending strain perpendicular to the wrinkles.This reveals that PDMS is an ideal substrate for magnetic films to realize flexible immutability.Our results may help for developing flexible magnetic devices.

A MAGNETO-MECHANICAL FULLY COUPLED MODEL FOR GIANT MAGNETOSTRICTION IN HIGH TEMPERATURE SUPERCONDUCTOR

This paper presents a fully coupled model to account for the flux pinning induced giant magnetostriction in type-Ⅱ superconductors under alternating magnetic field The superconductor E-J constitutive law is characterized by power law where the critical current density is assumed to depend exponentially on the flux density. The governing equations of the two-field problem （i.e., the interactions of elastic and magnetic effects） are formulated in a two-dimensional model. The magnetostriction curves and magnetization loops are calculated over a wide range of parameters. The effects of applied magnetic field frequency f and amplitude B0 and critical current density on magnetostriction and magnetization are discussed. Results show that the critical current density of high temperature superconductor （HTS） YBCO has a significant effect on the magnetization and magnetostriction. The pinning-induced magnetostriction which has been observed in experiment can be qualitatively simulated by this model.

铁磁纳米结构磁化状态及其磁-力耦合效应的相场模拟

基于随时间变化的Ginzburg-Landau(TDGL)方程,建立了模拟铁磁材料磁-力耦合效应的相场模型。从弱解形式出发,推导出了相关控制方程的有限元格式,然后编制程序进行数值求解。由于有限元对复杂边界有良好的适用性,该模型可用于不同形状铁磁材料的畴结构模拟。通过相场模拟,发现铁磁纳米结构中的磁化会形成涡旋结构,与实验观察到的磁化涡旋结构符合较好。由非均匀磁化引起的结构的变形、应力等力学参量都可以通过模拟一并得到。本文结果表明,改变结构形状可以有效控制磁畴结构的形态,适当的外应力可以改变磁畴结构及其对外磁性的大小。

Experimental and numerical study on surface roughness of magnetorheological elastomer for controllable friction

Magnetorheological elastomer (MRE) is a type of smart material of which mechanical and electrical properties can be reversibly controlled by the magnetic field. In this study, the influence of the magnetic field on the surface roughness of MRE was studied by the microscopic modeling method, and the influence of controllable characteristics of the MRE surface on its friction properties was analyzed by the macroscopic experimental method. First, on the basis of existing studies, an improved mesoscopic model based on magneto-mechanical coupling analysis was proposed. The initial surface morphology of MRE was characterized by the W–M fractal function, and the change process of the surface microstructures of MRE, induced by the magnetic interaction between particles, was studied. Then, after analyzing the simulation results, it is found that with the increase in the magnetic field and decrease in the modulus of rubber matrix, the surface of MRE changes more significantly, and the best particle volume fraction is within 7.5%–9%. Furthermore, through experimental observation, it is found that the height of the convex peak on the surface of MRE decreases significantly with the action of the magnetic field, resulting in a reduction in the surface roughness. Consistent with the simulation results, a particle volume fraction of 10% corresponds to a maximum change of 14%. Finally, the macroscopic friction experiment results show that the friction coefficients of MREs with different particle volume fractions all decrease with the decrease in surface roughness under the magnetic field. When the particle volume fraction is 10%, the friction coefficient can decrease by 24.7% under a magnetic field of 400 mT, which is consistent with the trend of surface roughness changes. This shows that the change in surface morphology with the effect of the magnetic field is an important factor in the control of MRE friction properties by magnetic field.