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Martensitic transformation in a two-dimensional polycrystalline shape memory alloys using a multi-phase-ﬁeld elasticity model based on pairwise rank-one convexiﬁed energies at small strain
For modeling the solid-solid transformation using the phase-ﬁeld method, we need to describe the phase-ﬁelds strain and stress ﬁelds in the interfacial regions which are necessary to deﬁne the mechanical driving force density of the phase-ﬁelds motion.Seeking quantitative modeling, we introduce brieﬂy a multi-phase-ﬁeld elasticity model based on the rank-one convexiﬁcation of the pairwise energies which satisﬁes the pairwise interfacial static equilibrium and kinematic compatibility conditions. As an application, we simulate the martensitic transformation in a two-dimensional polycrystalline SMAs at small strains. The ﬁnial evaluated microstructure consists of stress-free laminates meeting the theoretical expectations.