eXtended Variational Quasicontinuum Methodology for Lattice Networks with Damage and Crack Propagation

TL;DR

This paper extends the variational QuasiContinuum method to efficiently model crack propagation in lattice networks with damage, incorporating adaptive mesh refinement and enrichment functions for accurate crack path representation.

Contribution

It introduces a generalized variational QC methodology with new definitions for crack paths, enrichment functions, and summation rules for improved crack modeling in lattice networks.

Findings

Accurate crack paths captured in numerical examples.

Energy consistency maintained during mesh adaptivity.

Reaction forces and energy evolutions match direct simulations.

Abstract

Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully-resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.