SYMMETRIES OF 2-LATTICES AND SECOND ORDER ACCURACY OF THE CAUCHY–BORN MODEL

Abstract

Abstract. We show that the Cauchy–Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a gener-alization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys. 1