  The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and
Phillips in 1996, is a computational technique that can efficiently handle
regular atomistic lattices by combining continuum and atomistic approaches. In
the present work, the QC method is extended to irregular systems of particles
that represent a heterogeneous material. The paper introduces five QC-inspired
approaches that approximate a discrete model consisting of particles connected
by elastic links with axial interactions. Accuracy is first checked on simple
examples in two and three spatial dimensions. Computational efficiency is then
assessed by performing three-dimensional simulations of an L-shaped specimen
with elastic-brittle links. It is shown that the QC-inspired approaches
substantially reduce the computational cost and lead to macroscopic crack
trajectories and global load-displacement curves that are very similar to those
obtained by a fully resolved particle model.
