Recent experimental results show that apparent magneto-elastocaloric effect can be induced in the magnetostrictive-shape memory alloy composite system under an ultra-low magnetic field. In this paper, a multiscale theoretical model is constructed to predict the magneto-thermo-mechanically coupled response of such a composite system by considering the multi-field interactions among the heterogeneous constituent elements in the grain, polycrystalline aggregate and macroscopic scales. In the grain scale, for the magnetostrictive alloy (MEA), the fluctuations of stress and magnetic fields caused by the interactions among the domains are addressed by the self-consistent homogenization scheme. Adopting a probabilistic domain switching criterion based energetic analysis, a constitutive model of MEA is established. For the shape memory alloy (SMA), a crystal plasticity based thermo-mechanically coupled constitutive model is constructed in the framework of irreversible thermodynamics. The interactions among austenite phase and martensite variants are considered by the Mori-Tanaka's homogenization scheme. Thermodynamic driving force for martensite transformation and the internal heat production originated from transformation latent heat and inelastic deformation dissipation are derived from the dissipative inequality and the conservation of energy, respectively. In the polycrystalline aggregate scale, to estimate the interactions among the grains and predict the overall responses of the polycrystalline aggregates of MEA and SMA, a unified incremental magneto-thermo-mechanically coupled self-consistent homogenization scheme is developed. In the macroscopic scale, the magneto-thermo-mechanical interaction equations among the MEA rod, SMA cuboid and Al alloy frame in the composite system are derived by considering the conditions of deformation compatibility, force balance and thermodynamic equilibrium. The capability of the proposed multiscale model to describe the magneto-elastocaloric effect of MEA-SMA composite system is validated by comparing the predictions with the existing experimental data. Moreover, the influences of geometric dimension, pre-load, frame's stiffness and crystallographic orientation on the magneto-elastocaloric effect of the composite system are discussed. The proposed model provides a theoretical guidance for the optimization design of solid-state refrigeration devices in both the microscopic and macroscopic scales.

最近的实验结果表明，在超低磁场下，磁致伸缩-形状记忆合金复合体系可以产生明显的磁-弹性热效应。本文构建了一个多尺度理论模型来预测这种复合系统的磁-热-机械耦合响应，该模型考虑了晶粒、多晶骨料和宏观尺度中的异质组成元素之间的多场相互作用。在晶粒尺度上，对于磁致伸缩合金 (MEA)，由域之间的相互作用引起的应力和磁场的波动由自洽均质化方案解决。采用基于概率域切换准则的能量分析，建立了MEA的本构模型。对于形状记忆合金（SMA），在不可逆热力学的框架内构建了基于晶体塑性的热机械耦合本构模型。Mori-Tanaka 的均质化方案考虑了奥氏体相和马氏体变体之间的相互作用。马氏体相变的热力学驱动力和由相变潜热和非弹性变形耗散产生的内热分别来自耗散不等式和能量守恒。在多晶骨料尺度上，为了估计晶粒之间的相互作用并预测 MEA 和 SMA 多晶骨料的整体响应，开发了统一的增量磁-热-机械耦合自洽均化方案。在宏观尺度上，综合考虑变形相容性、力平衡和热力学平衡条件，推导出复合系统中MEA棒、SMA长方体和铝合金框架之间的磁-热-机械相互作用方程。通过将预测与现有实验数据进行比较，验证了所提出的多尺度模型描述 MEA-SMA 复合系统的磁弹性热效应的能力。此外，还讨论了几何尺寸、预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。复合材料系统中的SMA长方体和铝合金框架是通过考虑变形相容性、力平衡和热力学平衡条件推导出来的。通过将预测与现有实验数据进行比较，验证了所提出的多尺度模型描述 MEA-SMA 复合系统的磁弹性热效应的能力。此外，还讨论了几何尺寸、预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。复合材料系统中的SMA长方体和铝合金框架是通过考虑变形相容性、力平衡和热力学平衡条件推导出来的。通过将预测与现有实验数据进行比较，验证了所提出的多尺度模型描述 MEA-SMA 复合系统的磁弹性热效应的能力。此外，还讨论了几何尺寸、预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。力平衡和热力学平衡。通过将预测与现有实验数据进行比较，验证了所提出的多尺度模型描述 MEA-SMA 复合系统的磁弹性热效应的能力。此外，还讨论了几何尺寸、预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。力平衡和热力学平衡。通过将预测与现有实验数据进行比较，验证了所提出的多尺度模型描述 MEA-SMA 复合系统的磁弹性热效应的能力。此外，还讨论了几何尺寸、预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。讨论了预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。讨论了预载荷、框架刚度和晶体取向对复合系统磁弹性热效应的影响。所提出的模型为固态制冷装置的微观和宏观尺度的优化设计提供了理论指导。