Code for Geometry of Needle-Like Microstructures in Shape-Memory Alloysdoi:10.60507/FK2/VZAIVFbonndata2024-03-201Conti, Sergio; Lenz, Martin; Rumpf, Martin; Verhülsdonk, Jan; Zwicknagl, Barbara, 2024, "Code for Geometry of Needle-Like Microstructures in Shape-Memory Alloys", https://doi.org/10.60507/FK2/VZAIVF, bonndata, V1Code for Geometry of Needle-Like Microstructures in Shape-Memory Alloysdoi:10.60507/FK2/VZAIVFConti, SergioLenz, MartinRumpf, MartinVerhülsdonk, JanZwicknagl, Barbara211504053441211072390685813390873048bonndataVerhülsdonk, JanLenz, Martin2024-03-20Mathematical SciencesPhysicsThis 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.code<a href="https://mit-license.org/">MIT</a>Conti, S., Lenz, M., Rumpf, M., Verhülsdonk, J., Zwicknagl, B., Geometry of Needle-Like Microstructures in Shape-Memory Alloys. Shap. Mem. Superelasticity (2023)10.1007/s40830-023-00442-0Conti, S., Lenz, M., Rumpf, M., Verhülsdonk, J., Zwicknagl, B., Geometry of Needle-Like Microstructures in Shape-Memory Alloys. Shap. Mem. Superelasticity (2023)deformation.pytext/x-python-scriptenergy_density.pytext/x-python-scriptenvironment.ymlapplication/x-yamllicense.txttext/plainmain.pytext/x-python-scriptmesh_setup.pytext/x-python-scriptreadme.mdtext/markdownshape_optimization.pytext/x-python-script