中文摘要：

守恒定律与路径无关积分是传统力学中的重要工具，在位错、断裂力学和其他缺陷理论中具有重要的应用价值。由于力场和磁场的共同作用，以及磁弹性材料本身的耦合性质，所以磁弹性体具有更为广泛的守恒定律和路径无关积分。文中通过定义4种不同的热力学函数，应用电磁场理论中的能量矩概念，建立了磁弹性理论中对偶形式的守恒定律，并由这些对偶形式的守恒定律得到了相应的路径无关积分。文中建立的守恒定律和路径无关积分，对研究磁弹性体中的缺陷理论将起到十分重要的作用。

英文摘要：

Conservation laws and path-independent integrals are important tools in traditional mechanics, which have important applications in dislocation, fracture mechanics and defect theory.Due to the coupling action between stress field and magnetic field, and the coupling properties of magnetoelastic material, magnetoelasticity has more extensive conservation laws and path-independent integrals.By defining four different thermodynamic functions, and based on the concepts of energy-momentum tensor in electro-magnetic theory, the conservation laws and their dual forms in magnetoelasticity are established.The corresponding path-independent integrals in magnetoelasticity can be obtained .The conservation laws and path -independent integrals established in this paper could play an important role in studying defect theory in magnetoelasticity.