The paper focuses on numerical simulation of the phase-field (PF) equationsfor modeling martensitic transformations in shape memory alloys (SMAs), theircomplex microstructures and thermo-mechanical behavior. The PF model is basedon the Landau-Ginzburg potential for the 3D cubic-to-tetragonal phasetransformations in SMAs. The treatment of domain walls as diffuse interfaces,leads to a fourth-order differential equation in a strain-based order parameterPF model. The fourth-order equations introduce a number of unexplored numericalchallenges because traditional numerical schemes have been primarily applied tosecond-order problems. We propose isogeometric analysis (IGA) as a numericalformulation for a straightforward solution to the fourth-order differential PFequations using continuously differentiable non-uniform rational B-splines(NURBS). We present microstructure evolution in different geometries of SMAnanostructures under temperature-induced phase transformations to illustratethe geometrical flexibility, accuracy and robustness of our approach. Thesimulations successfully capture the dynamic thermo-mechanical behavior of SMAsobserved experimentally.
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