Multiscale Phase-Field Modeling of Fracture in Nanostructures

authored by: Mohsen Jahanshahi, Amir Reza Khoei, Niloofar Asadollahzadeh, Fadi Aldakheel
Abstract: The scientific community has witnessed, lately, a tremendous progress in the fabrication and synthesis of nanomaterials. As a result, it is essential to develop new and e±cient numerical techniques that are capable of modeling the behavior of materials at nanoscale with su±cient accuracy. In this work, a novel approach is presented for the multiscale analysis of brittle failure in nanostructures using the phase-field modeling. The specimen at microscale is discretized using finite elements (FEs), whose integration points lie in the representative volume elements (RVEs) at nanoscale. The displacement computed in upper scale for a microstructure that contains an evolving crack is imposed on the boundaries of the RVE in lower scale. On the other hand, the stresses and material properties obtained for the RVE in lower scale are transferred to upper scale to compute sti®ness matrices and load vectors. The evolution of the phase-field variable indicates the initiation and propagation of cracks at microscale. In order to avoid time-consuming molecular dynamics (MD) simulations at nanoscale in each step of the analysis, the Mooney–Rivlin material model is used to simulate the behavior of Aluminum (AL) nanostructure at this scale. The approach that is utilized to compute the material constants and the formulation for the multiscale technique combined with the phase-field modeling in upper scale are described in detail. It is discussed how the phase-field variable in microstructure is evolved based on the properties of the RVE in nanostructure. Many numerical examples are presented to demonstrate the application of the proposed multiscale technique in the solution of engineering problems.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): McGill University
Sharif University of Technology
Type: Article
Journal: Journal of Multiscale Modelling
Volume: 14
ISSN: 1756-9737
Publication date: 08.02.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Computer Science Applications
Electronic version(s): https://doi.org/10.1142/S1756973723500130 (Access: Closed)

BibTeX

@article{86d2d4126c284824ac44db374b36f0da,
title = "Multiscale Phase-Field Modeling of Fracture in Nanostructures",
abstract = "The scientific community has witnessed, lately, a tremendous progress in the fabrication and synthesis of nanomaterials. As a result, it is essential to develop new and e±cient numerical techniques that are capable of modeling the behavior of materials at nanoscale with su±cient accuracy. In this work, a novel approach is presented for the multiscale analysis of brittle failure in nanostructures using the phase-field modeling. The specimen at microscale is discretized using finite elements (FEs), whose integration points lie in the representative volume elements (RVEs) at nanoscale. The displacement computed in upper scale for a microstructure that contains an evolving crack is imposed on the boundaries of the RVE in lower scale. On the other hand, the stresses and material properties obtained for the RVE in lower scale are transferred to upper scale to compute sti{\textregistered}ness matrices and load vectors. The evolution of the phase-field variable indicates the initiation and propagation of cracks at microscale. In order to avoid time-consuming molecular dynamics (MD) simulations at nanoscale in each step of the analysis, the Mooney–Rivlin material model is used to simulate the behavior of Aluminum (AL) nanostructure at this scale. The approach that is utilized to compute the material constants and the formulation for the multiscale technique combined with the phase-field modeling in upper scale are described in detail. It is discussed how the phase-field variable in microstructure is evolved based on the properties of the RVE in nanostructure. Many numerical examples are presented to demonstrate the application of the proposed multiscale technique in the solution of engineering problems.",
keywords = "finite element method (FEM), hyperelasticity, molecular dynamics (MD), Multiscale method, phase-field modeling, representative volume element (RVE)",
author = "Mohsen Jahanshahi and Khoei, {Amir Reza} and Niloofar Asadollahzadeh and Fadi Aldakheel",
year = "2024",
month = feb,
day = "8",
doi = "10.1142/S1756973723500130",
language = "English",
volume = "14",
journal = "Journal of Multiscale Modelling",
issn = "1756-9737",
publisher = "World Scientific",
number = "4",
}