@Article{CoLeRu23,
  author = {Conti, Sergio and Lenz, Martin and Rumpf, Martin and Verh\"ulsdonk, Jan and Zwicknagl, Barbara},
  title  = {Geometry of Needle-Like Microstructures in Shape-Memory Alloys},
  journal = {Shap. Mem. Superelasticity},
  year = {2023},
  doi = {10.1007/s40830-023-00442-0},
  abstract = {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.}
}