Wednesday, March 28, 2012

1203.5854 (Brian Van Koten et al.)

Symmetries of 2-lattices and second order accuracy of the Cauchy--Born
Model
   [PDF]

Brian Van Koten, Christoph Ortner
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 generalization 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.
View original: http://arxiv.org/abs/1203.5854

No comments:

Post a Comment