Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

authored by: 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.
Organisation(s): Institute of Continuum Mechanics
Institute of Applied Mathematics
External Organisation(s): Swansea University
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 399
ISSN: 0045-7825
Publication date: 01.09.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.48550/arXiv.2205.13447 (Access: Open)
https://doi.org/10.1016/j.cma.2022.115358 (Access: Closed)
: Details in the research portal "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",
}