We rigorously derive a thin-film limit for martensitic crystals that utilizes the total variation of the deformation gradient to model the energy on surfaces separating regions of different variants. We find that the deformation for an infinitesimally thin film minimizes a two-dimensional energy.
Bibliographical noteFunding Information:
This work was supported in part by NSF DMS 95-05077, by NSF DMS-00-74043, by AFOSR F49620-98-1-0433, by ARO DAAG55-98-1-0335, by the Institute for Mathematics and its Applications, and by the Minnesota Supercomputer Institute.
- Bounded variation
- Surface energy
- Thin film