To model the mechanically-driven phase transformations, e.g. martensitic transformation, using the phase-field theory, suitable models are needed for describing the mechanical fields of the individual non-vanishing phase-fields in the interface regions in order to obtain the mechanical driving forces of phase-field motion. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions which have already been achieved in the literature for dual-phase-field materials by using the rank-one relaxation (or convexification) of the energy density. A direct generalization to the multi-phase-field case is not applicable without breaking these conditions partially. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields on their pairwise normals in triple and higher-order junctions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces...... (see PDF for the rest of the abstract)

翻译：为了利用相场理论模拟机械驱动的相变（例如马氏体相变），需要合适的模型来描述界面区域中各个非零相场的力学场，从而获得相场运动的机械驱动力。定量建模需要满足界面静力平衡和运动学兼容条件，这在文献中已通过能量密度的秩一松弛（或凸化）方法针对双相场材料实现。直接推广到多相场情况时，若不部分违背这些条件则无法适用。据我们所知，现有的多相场弹性模型均无法在三叉结点及更高阶结点处满足所有局部活跃相场在其成对法线方向上的跳跃条件。本文基于在成对界面上定义的弹性能量密度的部分秩一松弛，提出了一种新颖的多相场弹性模型……（其余摘要内容见PDF文件）