Quasicontinuum modeling of short-wave instabilities in crystal lattices

We propose a new hybrid quasicontinuum model which captures both long and short-wave instabilities of crystal lattices and combines the advantages of weakly nonlocal (gradient) and strongly nonlocal continuum models. To illustrate the idea we consider a simple one-dimensional lattice exhibiting commensurate and incommensurate short-wave instabilities and compute stability limits for the homogeneous phase using both discrete and quasicontinuum models. As we show, the quasicontinuum approximation is capable of reproducing a detailed structure of the discrete stability diagram.