4 problems

The case $d=3$ conjecture. Any non-polyconvex weak extremal $f\in {\cal C}_3$ is an extreme ray of ${\cal C}_3$. Moreover, if $f\in {\cal C}_3$ is a non-polyconvex extreme ray of…

Let $W\colon \operatorname{GL}^+(2)\to\mathbb{R}\cup\{+\infty\}$ be an objective, isotropic and rank-one convex function. For each $c\in\mathbb{R}$, define its sublevel set by … As…

For $F\in\mathbb{R}^{n\times n}$, define the exponentiated Hencky energy by … where $U$ is the right stretch tensor and $\mu,\kappa,k,\widehat{k}$ are parameters. Planar polyconvex…

For an isotropic elastic energy, let TSTS-M$^+$ denote the strict monotonicity of the Cauchy stress tensor with respect to the left Hencky strain, in the sense that the correspondi…