A hybrid quasicontinuum method
A. Kavalur and W. K. Kim
International Journal for Numerical Methods in Engineering, 117, 1059–1078 (2019).


Quasicontinuum (QC) is a partitioned-domain multiscale method where the full-atomistic description is retained in highly deformable subdomains while the energy in the remaining region is approximated using a continuum constitutive relation called the Cauchy-Born (CB) rule. While the CB rule can capture the full nonlinearity of the strain energy, its computational cost is one or two orders of magnitude higher than the linear elasticity (LE) constitutive relation. In this paper, we propose an extension to the QC method, referred to as "hybrid QC," where both the CB and LE relations are combined to increase the efficiency of the original QC method. This extension is summed up to a two-step process. First, the continuum region is further divided into subregions with CB being restricted to subregions adjoining the atomistic region while LE is adopted in the remaining subregions. Second, a corrective scheme is applied to the LE subregion to recover the higher-order accuracy. The hybrid QC method is validated through two examples: (i) a crystal containing a dipole of Lomer dislocations and (ii) a nanoindentation system. The simulation results show that the proposed hybrid QC method is numerically more efficient than the original QC method while maintaining virtually the same accuracy.