Davit Harutyunyan, davith@math.utah.edu
Co-authors: Graeme W.Milton
Examples of extremal quasiconvex quadratic forms that are not polyconvex
We prove that if the associated fourth order tensor of a quadratic form has a linear elastic cubic symmetry then
it is a quasiconvex form if and only if it is polyconvex, i.e., a sum of convex and null–Lagrangian quadratic
forms. We prove that allowing for slightly less symmetry, namely only cyclic and axis–reflection symmetry,
gives rise to a class of extremal quasiconvex quadratic forms, that also turn out to be non–polyconvex.