An axisymmetric and axially homogenous variational formulation is presented for coupled extension-torsion-inflation deformation in compressible magnetoelastomeric tubes in the presence of azimuthal and axial magnetic fields. The tube’s material is assumed to have a preferred magnetization direction which lie in the radial plane but at an angle from the tube’s axial direction - this imparts helical magnetic anisotropy to the tube. The governing differential equations necessary to solve the above deformation problem are obtained which are shown to reduce to a set of nonlinear algebraic equations in the thin tube limit. This allows us to obtain analytical expressions in terms of the applied magnetic field, preferred magnetization direction and magnetoelastic constants which tell us how these parameters can be tuned to generate unusual coupled deformations such as negative Poisson’s effect. The study can be useful in designing magnetoelastic soft tubular actuators.

中文翻译：

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具有螺旋磁各向异性的可压缩磁弹性细管中的拉伸-扭转-膨胀耦合

在存在方位角和轴向磁场的情况下，针对可压缩磁弹性管中的耦合拉伸-扭转-膨胀变形，提出了一种轴对称和轴向均匀变分公式。假定管的材料具有优选的磁化方向，该方向位于径向平面但与管的轴向方向成一定角度——这赋予管螺旋磁各向异性。获得解决上述变形问题所必需的控制微分方程，这些方程被证明可以简化为细管极限中的一组非线性代数方程。这使我们能够获得外加磁场的解析表达式，首选磁化方向和磁弹性常数告诉我们如何调整这些参数以产生不寻常的耦合变形，例如负泊松效应。该研究可用于设计磁弹性软管致动器。