# Quasicontinuum Method Extended to Irregular Lattices

## TL;DR

This paper extends the quasicontinuum method to irregular particle systems in heterogeneous materials, introducing five approaches that improve computational efficiency while maintaining accuracy in simulating crack propagation.

## Contribution

The work develops five QC-inspired methods for irregular lattices, enabling efficient and accurate simulations of heterogeneous materials with complex crack behavior.

## Key findings

- Significant reduction in computational cost.
- High accuracy in crack trajectory prediction.
- Close agreement with fully resolved particle models.

## Abstract

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.