Computation of length scales for second-order laminated microstructure with surface energy

A computational model for the total energy, including surface energy, of second-order laminated microstructures is proposed. By studying the minimization property of this energy, we can numerically reveal how the twin widths of a second-order laminated microstructure are related to the specimen's length and the surface energy density of a crystalline material. Numerical experiments on a two-dimensional Ericksen-James type elastic model for crystals show that the twin widths of the first and second-order laminates satisfy certain cubic rule.