Magnetostrictive materials that couple mechanical and magnetic domains have been widely explored for use in sensors and actuators. These materials often exhibit a nonlinear material response under applied magnetic fields, which limits the use of linear constitutive models. Furthermore, the nonlinear constitutive relations tend to be implicit in nature. Hence, a finite element scheme that can handle the implicit relationship between the mechanical (stresses and strains) and magnetic (magnetic flux density and magnetic field) quantities is proposed in order to arrive at solutions to boundary value problems. In the proposed scheme, while the physical requirements of equilibrium and strain–displacement relation are satisfied point-wise, the constitutive relations hold in a weak integral sense. A fully coupled magnetostrictive plane stress rectangular element is developed based on the proposed scheme and its efficacy in arriving at solutions to coupled field boundary value problems is illustrated by subjecting the element to standard loading conditions.

中文翻译：

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隐式磁致伸缩本构关系的有限元公式

耦合机械和磁畴的磁致伸缩材料已被广泛探索用于传感器和执行器。这些材料在外加磁场下通常表现出非线性材料响应，这限制了线性本构模型的使用。此外，非线性本构关系在本质上往往是隐含的。因此，提出了一种可以处理机械量（应力和应变）和磁量（磁通密度和磁场）之间隐含关系的有限元方案，以便得出边值问题的解决方案。在所提出的方案中，虽然平衡和应变-位移关系的物理要求是逐点满足的，但本构关系在弱积分意义上成立。