An adaptive variational Quasicontinuum methodology for lattice networks with localized damage

TL;DR

This paper introduces an adaptive variational Quasicontinuum method for lattice networks that efficiently models crack initiation and growth in materials like 3D-printed structures and foams, balancing accuracy and computational cost.

Contribution

It develops an adaptive multiscale QC approach for damageable lattices, enabling efficient and accurate simulation of evolving fractures in complex materials.

Findings

The adaptive scheme maintains energy consistency.

The method accurately predicts crack propagation.

Computational efficiency is significantly improved.

Abstract

Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso-structures of materials such as 3D-printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non-locality, large deformations, and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering-scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy-consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes, and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem.