10.60507/FK2/VZAIVFConti, SergioSergioConti0000-0001-7987-9174University of BonnLenz, MartinMartinLenz0000-0002-5394-6874University of BonnRumpf, MartinMartinRumpf0000-0001-6049-9390University of BonnVerhülsdonk, JanJanVerhülsdonk0009-0008-9466-505XUniversity of BonnZwicknagl, BarbaraBarbaraZwicknagl0000-0002-6394-0775University of Bonnbonndata2024Mathematical SciencesPhysicsVerhülsdonk, JanJanVerhülsdonkUniversity of Bonn2024-03-202024-03-22code10.1007/s40830-023-00442-04180139440310648638974516974262text/x-python-scripttext/x-python-scriptapplication/x-yamltext/plaintext/x-python-scripttext/x-python-scripttext/markdowntext/x-python-script1.1MITThis repository contains the code to <a href="https://doi.org/10.1007/s40830-023-00442-0">Conti, S., Lenz, M., Rumpf, M., Verhülsdonk, J., Zwicknagl, B., Geometry of Needle-Like Microstructures in Shape-Memory Alloys. Shap. Mem. Superelasticity (2023).</a> Needle-like microstructures are often observed in shape memory alloys near macro-interfaces that separate regions with different laminate orientation. We study their shape with a two-dimensional model based on nonlinear elasticity, that contains an explicit parametrization of the needle profiles. Energy minimization leads to specific predictions for the geometry of needle-like domains. Our simulations are based on shape optimization of the needle interfaces, using a polyconvex energy density with cubic symmetry for the elastic problem, and a numerical implementation via finite elements on a dynamically changing grid.Deutsche Forschungsgemeinschaft (DFG)211504053Deutsche Forschungsgemeinschaft (DFG)441211072Deutsche Forschungsgemeinschaft (DFG)390685813Deutsche Forschungsgemeinschaft (DFG)390873048