A Unified Variational Setting and Algorithmic Framework for Mono- and Polycrystalline Martensitic Phase Transformations
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The unified setting presented here is based on phase transformations (PTs) of monocrystalline shape memory alloys (SMAs) and includes polycrystalline SMAs whose microstructure is modeled using lattice variants of RVEs consisting of equal convex isotropically elastic grains. A pre-averaging scheme for randomly distributed polycrystalline variants of PT-strains is used transforming them into those of a fictitious monocrystal. A major point is the overall finite element based integration algorithm in time and space for both mono- and polycrystalline PTs with differences only on the material level, whereas the parametric time integration with quasi-convexification and the solution algorithm in space remains the same. Examples for full PT cycles and comparisons with experiment are presented.
KeywordsShape Memory Alloy Representative Volume Element Gauss Point Martensitic Phase Transformation Shape Memory Alloy Behavior
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