Voronoi tessellation based statistical volume element characterization for use in fracture modeling

Acton, Katherine; Baxter, Suzanne Domel; Bahmani, Bahador; Clarke, Philip L.; Abedi, Reza

doi:10.1016/j.cma.2018.02.025

Cited by 23 publications

(5 citation statements)

References 52 publications

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“…In the present work, among strength, energy, and initial damage parameters, we consider inhomogeneity only in the strength property. This is in accord with a majority of similar studies in the literature such as [55][56][57][58][59][60].…”

Section: Realization Of Stochastic Damage Model Parameterssupporting

confidence: 92%

“…We treat cohesion as a stationary random field with certain standard deviation ς c and correlation length l c . The statistics of this random field can be systematically obtained by using Statistical Volume Elements (SVEs), as shown in [60,61]. However, for simplicity and better control on the effect of these parameters, we artificially manufacture random fields with certain ς c and l c .…”

Section: Realization Of Stochastic Damage Model Parametersmentioning

confidence: 99%

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A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture

2019

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We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture.

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Section: Realization Of Stochastic Damage Model Parameterssupporting

confidence: 92%

Section: Realization Of Stochastic Damage Model Parametersmentioning

confidence: 99%

A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture

2019

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“…This particular setting ensures consistency with critical subscale information and allows for the propagation of stochasticity at the macroscopic level. Similar ideas were pursed in the very recent work, with a few noticeable differences though. First, the approach developed in the aforementioned reference is concerned with dynamical fracture, solved using an asynchronous spacetime discontinuous Galerkin method, and is focused on fracture strength random fields.…”

Section: Introductionmentioning

confidence: 60%

“…Second, while both contributions invoke information theory as a rationale to define probability measures, stochastic modeling aspects and related methodological issues are addressed more extensively hereinafter. Note also that crack paths are simulated in the sequel by propagating a pre-existing crack, whereas crack nucleation sites are identified, for each sample of the microstructure, as the weakest material points in the work of Acton et al 19 This paper is organized as follows. The computational approach enabling the description of crack propagation at the microscopic scale is first detailed in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Stochastic multiscale modeling of crack propagation in random heterogeneous media

Hun

Guilleminot

Yvonnet

et al. 2019

Numerical Meth Engineering

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Summary A stochastic approach to model crack propagation in random heterogeneous media, using mesoscopic representations of elastic and fracture properties, is presented. In order to obtain reference results, Monte‐Carlo simulations are first conducted on microstructural samples in which a pre‐existing crack is propagated by means of a phase‐field approach. These computations are used to estimate the subscale‐induced randomness on the macroscopic response of the domain. Mesoscopic descriptors are then introduced to investigate scale transition. Elasticity tensor random fields are specifically defined, at that stage, through a moving‐window upscaling approach. The mesoscopic fracture toughness, which is assumed homogeneous and deterministic, is identified by solving an inverse problem involving the macroscopic peak force. A stochastic model is subsequently constructed in which the mesoscopic elasticity is described as a non‐Gaussian random field. This model allows the multiscale‐informed elastic counterpart in the phase‐field formulation to be sampled without resorting to computational homogenization. The results obtained with the sample‐based and model‐based mesoscopic descriptions are finally compared with those corresponding to the full‐scale microscopic model. It is shown, in particular, that the mesoscopic elasticity‐phase‐field formulation associated with statically uniform boundary conditions enables the accurate predictions of the mean elastic response and mean peak force.

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“…Few other multiscale approaches for concrete modeling considering adaptive homogenization of lattice discrete particle model, deriving the stress intensity factor by process zone mechanism, bridging the constitutive damage formulation of mesoscale and microscale to obtain effective properties of mesoscopic under the micro cracked solid, statistical volume element, stochastic damage model and state equation of cement paste/mortar are (Acton et al., 2018; Feng et al., 2018; Hun et al., 2019; Rezakhani et al., 2017; Santosh and Ghosh, 2015; Sencu et al., 2016; Simon and Chandra Kishen, 2017; Tal and Fish, 2018; Zhu et al., 2017; Zhutovsky et al., 2018).…”

Section: Discussionmentioning

confidence: 99%

A review of continuum damage and plasticity in concrete: Part I – Theoretical framework

Park

Ahmed

Voyiadjis

2021

International Journal of Damage Mechanics

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In the past few decades, extensive research on concrete modeling to predict behavior, crack propagation, microcrack coalescence by utilizing different approaches (fracture mechanics, continuum damage mechanics) were investigated theoretically and numerically. The presented paper aims to review the theoretical work of continuum concrete damage and plasticity modeling in part I of the work. The detailed theoretical work is presented with some of the supporting work related to multiscale modeling and phase-field modeling is also part of this paper. Few other applications related to rate-dependent models and fatigue in concrete are also discussed. In part II of this work, the review of numerical work limited to finite element is presented. Some open issues in concrete damage modeling and future research needed are also discussed in part II.

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Voronoi tessellation based statistical volume element characterization for use in fracture modeling

Cited by 23 publications

References 52 publications

A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture

A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture

Stochastic multiscale modeling of crack propagation in random heterogeneous media

A review of continuum damage and plasticity in concrete: Part I – Theoretical framework

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