Polyconvex double well functions
We investigate polyconvexity of the double well function $f(X) := |X-X_1|^2|X-X_2|^2$ for given matrices $X_1, X_2 \in \R^{n \times n}$. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. We prove that $f$ is polyconvex if and only if the … Read more