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
M. Sarhil, O. Shchyglo, D. Brands, I. Steinbach, J. Schröder.
Proceedings in Applied Mathematics & Mechanics, Wiley-VCH GmbH, 20, 1-3, (2021)
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.
Cite as: https://doi.org/10.1002/pamm.202000200