Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale
schemes that combine the accuracy of atomistic models with the efficiency of continuum …

This paper addresses the problem of consistent energy-based coupling of atomistic and
continuum models of materials, limited to zero-temperature statics of simple crystals. It has …

Many materials can be modeled either as discrete systems or as continua, depending on the
scale. At intermediate scales it is necessary to understand the transition from discrete to …

For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a
posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented …

We analyze a force-based quasicontinuum approximation to a one-dimensional system of
atoms that interact by a classical atomistic potential. This force-based quasicontinuum …

The accuracy of the quasi-continuum method is analyzed using a series of models with
increasing complexity. It is demonstrated that the existence of the ghost force may lead to …

Due to their algorithmic simplicity and high accuracy, force-based model coupling
techniques are popular tools in computational physics. For example, the force-based …

The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces
under uniform strain that have been called ghost forces. In this paper, we prove for a …

We investigate the stability of Bravais lattices and their Cauchy–Born approximations under
periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born …

The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries,
occurs when the lattice configuration loses stability, that is, when an eigenvalue of the …