Code for Geometry of Needle-Like Microstructures in Shape-Memory Alloys

This 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.