标题： 有限变形磁粘弹性理论 显示英文标题

标题： A theory of finite deformation magneto-viscoelasticity

摘要： 本文涉及大应变磁粘弹性变形的数学建模。 能量耗散被假设既由于机械粘弹性效应，也由于材料对磁化的阻力。 通过将变形梯度和磁感应分解为“弹性”和“粘性”部分，考虑了体内内部阻尼机制的存在。 推导了材料行为的本构定律以及非平衡场的演化方程，这些方程符合热力学定律。 为了说明该理论，提出了应力松弛、磁场松弛、时间依赖的磁感应和应变问题，并针对本构定律的一种具体形式进行了求解。 结果以图形方式展示了多个建模参数对变形和磁化过程的影响。 显示英文摘要

摘要： This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to magnetisation. Existence of internal damping mechanisms in the body is considered by decomposing the deformation gradient and the magnetic induction into `elastic' and `viscous' parts. Constitutive laws for material behaviour and evolution equations for the non-equilibrium fields are derived that agree with the laws of thermodynamics. To illustrate the theory the problems of stress relaxation, magnetic field relaxation, time dependent magnetic induction and strain are formulated and solved for a specific form of the constitutive law. The results, that show the effect of several modelling parameters on the deformation and magnetisation process, are illustrated graphically.