Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

verfasst von: Nima Noii, Amirreza Khodadadian, Fadi Aldakheel
Abstract: A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and spatial quantities (of different phases in the geometrical domain) are assumed to be homogeneous and deterministic. This is unlike the lower scale with strong fluctuation in the material and geometrical properties. Such a response is approximated through some uncertainty in the model problem. The presented contribution is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure. Hereby, the proposed model employs various representative volume elements with random distribution of stiff inclusions and voids within the composite structure. We develop an allocating strategy to allocate the heterogeneities and generate the corresponding meshes in two- and three-dimensional cases. Then the Monte Carlo Finite Element Method (MC-FEM) is employed for solving the stochastic PDE-based model and approximate the expectation and the variance of the solution field of brittle/ductile failure by evaluating a large number of samples. For the prediction of failure mechanisms, we rely on the phase-field approach which is a widely adopted framework for modeling and computing the fracture phenomena in solids. Incremental perturbed minimization principles for a class of gradient-type dissipative materials are used to derive the perturbed governing equations. This analysis enables us to study the highly heterogeneous microstructure and monitor the uncertainty in failure mechanics. Several numerical examples are given to examine the efficiency of the proposed method.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Institut für Angewandte Mathematik
Externe Organisation(en): Swansea University
Typ: Artikel
Journal: Computer Methods in Applied Mechanics and Engineering
Band: 399
ISSN: 0045-7825
Publikationsdatum: 01.09.2022
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2205.13447 (Zugang: Offen)
https://doi.org/10.1016/j.cma.2022.115358 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{55253deb727440459ba3710ee7e5f780,
title = "Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures",
abstract = "A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and spatial quantities (of different phases in the geometrical domain) are assumed to be homogeneous and deterministic. This is unlike the lower scale with strong fluctuation in the material and geometrical properties. Such a response is approximated through some uncertainty in the model problem. The presented contribution is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure. Hereby, the proposed model employs various representative volume elements with random distribution of stiff inclusions and voids within the composite structure. We develop an allocating strategy to allocate the heterogeneities and generate the corresponding meshes in two- and three-dimensional cases. Then the Monte Carlo Finite Element Method (MC-FEM) is employed for solving the stochastic PDE-based model and approximate the expectation and the variance of the solution field of brittle/ductile failure by evaluating a large number of samples. For the prediction of failure mechanisms, we rely on the phase-field approach which is a widely adopted framework for modeling and computing the fracture phenomena in solids. Incremental perturbed minimization principles for a class of gradient-type dissipative materials are used to derive the perturbed governing equations. This analysis enables us to study the highly heterogeneous microstructure and monitor the uncertainty in failure mechanics. Several numerical examples are given to examine the efficiency of the proposed method.",
keywords = "Brittle/ductile fracture, Monte Carlo simulation, Phase-field model, Probabilistic failure, Random distribution",
author = "Nima Noii and Amirreza Khodadadian and Fadi Aldakheel",
note = "Funding Information: The corresponding author Fadi Aldakheel (FA) appreciates the scientific support of the German Research Foundation in the priority program, GermanySPP 2020 (Project Number: 353757395). FA would like to thank professors Michael Haist and Ludger Lohaus (www.baustoff.uni-hannover.de) for providing the computer tomography CT-images of concrete microstructure (Fig. 1), which represents an application of the segmentation tolerance (perturbations) in the geometrical properties. Professor Peter Wriggers (www.ikm.uni-hannover.de) detailed comments and suggestions are highly acknowledged.",
year = "2022",
month = sep,
day = "1",
doi = "10.48550/arXiv.2205.13447",
language = "English",
volume = "399",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}