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In this article we present a comparative analysis of different versions of the quasicontinuum method, which aim at a seamless transition from the atomistic to the continuum description of crystalline solids at zero temperature. All versions of this popular and powerful method exhibit the same building blocks, namely (i) a coarse-graining of fully atomistic resolution via kinematic constraints, (ii) an approximation of the energy/forces in coarse-grained regions via numerical quadrature and (iii) adaptive mesh refinement. The quasicontinuum versions are assessed in an example where a Lomer dislocation dipole is subject to shear deformation. In a second example, the fully nonlocal quasicontinuum method is used to simulate nanoindentation into an fcc single crystal. Compared with lattice statics good agreement is achieved with respect to significant details of the material behaviour for a small fraction of the computational costs.

Coupling atomistic accuracy with continuum effectivity for predictive simulations in materials research – the Quasicontinuum Method