Extended quasicontinuum methodology for highly heterogeneous discrete systems

Benjamin Werner (Corresponding author), Jan Zeman, Ondřej Rokoš

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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.

Originele taal-2Engels
TijdschriftInternational Journal for Numerical Methods in Engineering
Nummer van het tijdschrift6
Vroegere onlinedatum27 dec. 2023
StatusGepubliceerd - 30 mrt. 2024


The work of Benjamin Werner received funding from projects No. CZ.02.2.69/0.0/0.0/ 18_053/0016980 awarded by the Ministry of Education, Youth and Sports of the Czech Republic (from 02/2021 to 04/2022), No. 22‐35755K awarded the Czech Science Foundation (from 01/2023) and by the CTU Global PostFellowship Program (from 05/2022). The work of Jan Zeman and Ondřej Rokoš was supported by project No. 19‐26143X awarded by the Czech Science Foundation.

Czech Technical University05/2022
Ministerstvo Školství, Mládeže a Tělovýchovy04/2022
Grantová Agentura České Republiky01/2023


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