Extended quasicontinuum methodology for highly heterogeneous discrete systems
B. Werner, J. Zeman J and O. Rokoš
International Journal for Numerical Methods in Engineering, 125, e7415 (2024).

ABSTRACT
Lattice networks are indispensable to study heterogeneous materials such as
concrete or rock as well as textiles and woven fabrics. Due to the discrete
character of lattices, they quickly become computationally intensive. The
QuasiContinuum (QC) Method resolves this challenge by interpolating the
displacement of the underlying lattice with a coarser finite element mesh and
sampling strategies to accelerate the assembly of the resulting system of
governing equations. In lattices with complex heterogeneous microstructures with
a high number of randomly shaped inclusions the QC leads to an almost
fully-resolved system due to the many interfaces. In the present study the QC
Method is expanded with enrichment strategies from the eXtended Finite Element
Method (XFEM) to resolve material interfaces using nonconforming meshes. The
goal of this contribution is to bridge this gap and improve the computational
efficiency of the method. To this end, four different enrichment strategies are
compared in terms of their accuracy and convergence behavior. These include the
Heaviside, absolute value, modified absolute value and the corrected XFEM
enrichment. It is shown that the Heaviside enrichment is the most accurate and
straightforward to implement. A first-order interaction based summation rule is
applied and adapted for the extended QC for elements intersected by a material
interface to complement the Heaviside enrichment. The developed methodology is
demonstrated by three numerical examples in comparison with the standard QC and
the full solution. The extended QC is also able to predict the results with 5%
error compared to the full solution, while employing almost one order of
magnitude fewer degrees of freedom than the standard QC and even more compared
to the fully-resolved system.