The Gamma-Convergence of a Sharp Interface Thin Film Model with Nonconvex Elastic Energy
Pavel Bělı́k, Mitchell Luskin · SIAM Journal on Mathematical Analysis · 2006
We give results for the $\Gamma$-limit of a scaled elastic energy of a film as the thickness $h>0$ converges to zero. The elastic energy density models materials with multiple phases or variants and is thus nonconvex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.