Size effect analysis of quasi-brittle fracture with localizing gradient damage model

Zhang, Yi; Shedbale, A. S.; Gan, Yixiang; Moon, Juhyuk; Poh, Leong Hien

doi:10.1177/1056789520983872

Cited by 17 publications

(8 citation statements)

References 47 publications

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“…Extensive research of this model is presented in [ 31 ], also in the context of verification using different examples, not only for concrete, but also for other composite materials. As shown in [ 32 ], the model is able to reproduce the size effect. The Ottosen equivalent strain measure as an alternative loading function [ 33 ] can be applied in the LGD model to simulate properly a mixed-mode concrete cracking.…”

Section: Introductionmentioning

confidence: 85%

Survey of Localizing Gradient Damage in Static and Dynamic Tension of Concrete

Wosatko

2022

Materials

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The continuum damage model should be regularized to ensure mesh-insensitive results in simulations of strain localization, e.g., for concrete cracking under tension. The paper confronts the conventional gradient damage model with its upgrade including a variable internal length scale. In these models, the Helmholtz free energy depends additionally on an averaged strain measure and its gradient. In the formulation for dynamics the equations of motion are discretized simultaneously with an averaging equation. If gradient regularization is employed with a constant internal length parameter, then an artificially expanded damage zone can occur in the strain softening analysis. This broadening effect can be inhibited by a gradient activity function. The localizing character of the gradient activity has physical motivation—the nonlocal interactions in the fracture zone are reduced with the damage growth. The internal length can decrease exponentially or as a cosine function. After presentation of the theory, including the free energy definition, the finite element analyses of three different examples connected with tensile cracking in concrete are discussed: static tension of a double-edge-notched specimen, dynamic direct tension for a configuration without or with a reinforcing bar and tension of an L-shaped specimen under static and dynamic loading.

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Section: Introductionmentioning

confidence: 85%

Survey of Localizing Gradient Damage in Static and Dynamic Tension of Concrete

Wosatko

2022

Materials

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“…Few other phase-field approaches for modeling interface damage with crack propagation in microstructures, unified phase-field theory for quasi-brittle damage and mechanics of damage, numerical implementation of phase-field damage model, an iterative scheme for a phase-field model with implementation in Abaqus, variational consistent phase-field anisotropic damage model and comprehensive implementation in Abaqus by using three approaches (UMAT-Modified Newton solver, UEL-Staggered, and UEL-QuasiNewton monolithic) are presented by (Nguyen et al., 2016; Wang et al., 2021; Wu, 2017, 2018b; Wu et al., 2020b; Wu and Huang, 2020; Zhang et al., 2018, 2019a).…”

Section: Recent Advancements In Phase-field Modelingmentioning

confidence: 99%

“…As the damage evolution is not captured well, the conventional nonlocal approach cannot predict the size effect in concrete. To overcome this, localizing gradient enhancement is presented by (Zhang et al, 2021) to avoid spurious damage growth and capture the size effect. Giry et al (2011) modified the nonlocal integral based formulation by proposing the stress-based nonlocal interaction domain.…”

Section: Regularization Of Local Variablementioning

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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“…The localizing gradient enhancement was shown to work well for different problems, e.g. quasi-static fracture of quasi-brittle materials (Castillo et al., 2021; Sarkar et al., 2019; Shedbale et al., 2021; Tong et al., 2021b), size effects in quasi-brittle fracture (Negi et al., 2021; Zhang et al., 2021), thermo-mechanical fracture (Sarkar et al., 2020), continuous-discontinuous modelling (Sarkar et al., 2021), dynamic fracture (Wang et al., 2019) and ductile fracture (Xu et al., 2020; Xu and Poh, 2019).…”

Section: Introductionmentioning

confidence: 99%

A simple implementation of localizing gradient damage model in Abaqus

Zhang

Wang

et al. 2022

International Journal of Damage Mechanics

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With the localizing gradient enhancement, a damage model for quasi-brittle materials is able to achieve regularized softening responses, with localized damage profiles corresponding to the development of macroscopic cracks, to resolve the numerical spurious effects induced by the conventional gradient enhancement. The typical implementation strategy for a gradient enhanced model is to solve the system of governing equations simultaneously. Focusing on the finite element (FE) package Abaqus, a user element subroutine is required to define the finite elements with additional degrees of freedom for the nonlocal field. Moreover, with user elements, additional effort is required to visualize the numerical results. To an inexperienced engineer/researcher, these requirements can be challenging. In this paper, a simple implementation of the localizing gradient damage model is elaborated. By utilizing the in-built coupled thermo-mechanical elements in Abaqus, the user only needs to define the material constitutive laws, as well as the sensitivity terms with respect to the field variables. Post-processing of results can be done directly in Abaqus. The applicability and ease of implementation are demonstrated via several examples, including those that utilize the Abaqus features of element deletion, contact between surfaces, as well as the incorporation of cohesive elements. Sample files can be downloaded from https://github.com/leonghien/Localizing-Gradient-Damage-with-UMAT-UMATHT

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Size effect analysis of quasi-brittle fracture with localizing gradient damage model

Cited by 17 publications

References 47 publications

Survey of Localizing Gradient Damage in Static and Dynamic Tension of Concrete

Survey of Localizing Gradient Damage in Static and Dynamic Tension of Concrete

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

A simple implementation of localizing gradient damage model in Abaqus

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