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. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Sarhil, Mohammad; Shchyglo, Oleg; Brands, Dominik; Steinbach, Ingo; Schröder, Jörg
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000200
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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.