Studies of dynamic crack propagation and crack branching with peridynamics

Ha, Youn Doh; Bobaru, Florin

doi:10.1007/s10704-010-9442-4

Cited by 616 publications

(214 citation statements)

References 30 publications

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“…Kilic and Madenci [120,121] studied structural stability and failure analysis, and in that work peridynamics was used to predict crack paths in a quenched glass plate. Some other studies have been conducted in fracture mechanics using peridynamics [122][123][124][125], and peridynamics has also been applied to study composites [126][127][128][129].…”

Section: Peridynamicsmentioning

confidence: 99%

Multiscale modeling and simulation of rolling contact fatigue

Gharehbagh

Ali

2018

International Journal of Fatigue

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iii ABSTRACT In this thesis, a hierarchical multiscale method was developed to predict rolling contact fatigue lives of mechanical systems. In the proposed multiscale method, the molecular modeling and simulation of lubricant was conducted to investigate the friction between rolling contact surfaces. The calculated friction coefficient was passed to the continuum model of rolling contact components to predict fatigue lives.Molecular dynamics modeling and simulation of thin film lubrication and lubricated contact surfaces were carried out to investigate mechanisms of hydrodynamic lubrication at nano-scale first. Although various lubricant alkane chains were considered in the molecular model, the chain length of eight united molecules were mainly employed in this thesis. In addition, the effects of temperature and nano-particles (debris) on the friction forces were discussed. It was found that the existing of nano-particles (debris) could increase the friction force between contact surfaces with hydrodynamic lubrication.In the continuum model of the developed multiscale method, finite element analysis was employed to predict rolling contact fatigue life of rolling contact components, including bearing and gear-tooth. Specifically, the fatigue crack initiation of bearing was studied, and then the fatigue crack initiation and propagation in gear-tooth. In addition, the enhancement of gear-tooth fatigue life by using composite patches was discussed as well. It should be noted that the friction coefficient used in the continuum model was calculated in the molecular model. It is one-way message passing in iv the developed multiscale method.Another continuum method was studied and developed in this thesis to provide alternate methods for the continuum model in the proposed multiscale framework.Peridynamics method has advantages in modeling and simulation of discontinuities, including cracks, over the conventional finite element methods. The applications of Peridynamics in predicting fatigue crack initiation and propagation lives were discussed in this thesis. v PUBLIC ABSTRACTThis research aims to develop a hierarchical multiscale method to predict rolling contact fatigue lives of mechanical systems. In the proposed multiscale method, the molecular modeling and simulation of lubricant was conducted to investigate the friction between rolling contact surfaces. The calculated friction coefficient was passed to the continuum model of rolling contact components to predict fatigue lives.Molecular dynamics modeling and simulation of thin film lubrication and lubricated contact surfaces were carried out to investigate mechanisms of hydrodynamic lubrication at nano-scale first. In addition, the effects of temperature and nano-particles (debris) on the friction forces were discussed. It was found that the existing of nanoparticles (debris) could increase the friction force between contact surfaces with hydrodynamic lubrication.In the continuum model of the developed multiscale method, finite element analysis was employed to pred...

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Section: Peridynamicsmentioning

confidence: 99%

Multiscale modeling and simulation of rolling contact fatigue

Gharehbagh

Ali

2018

International Journal of Fatigue

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“…At scales much larger than the horizon size, the specific shape of the micromodulus function has little influence. The shape of the micro-conductivity function also plays a role in terms of numerical approximations, as shown in, e.g., [22,23] for the micromodulus function in the mechanical peridynamic model.…”

Section: The Micro-conductivity Functionmentioning

confidence: 99%

“…where μ is a history-dependent scalar-valued function defined by if e (τ, ξ, η) < e 0 (10) otherwise Here, (11) is the "relative elongation" of a bond, e 0 is the critical relative elongation of the bond, ξ = x -x is the relative position vector in the initial configuration and η = u(x , t) -u (x, t) is the relative displacement vector (see, e.g., [23,25]). The scalar-valued function α is zero if the crack can be assimilated with an insulated crack, and is a sub-unitary number if conduction is only partially reduced by the crack formed.…”

Section: A Thermal Materials With Damagementioning

confidence: 99%

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

Bobaru

Duangpanya

2012

Journal of Computational Physics

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257

142

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We introduce a multidimensional peridynamic formulation for transient heat-transfer. The model does not contain spatial derivatives and uses instead an integral over a region around a material point. By construction, the formulation converges to the classical heat transfer equations in the limit of the horizon (the nonlocal region around a point) going to zero. The new model, however, is suitable for modeling, for example, heat flow in bodies with evolving discontinuities such as growing insulated cracks. We introduce the peridynamic heat flux which exists even at sharp corners or when the isotherms are not smooth surfaces. The peridynamic heat flux coincides with the classical one in simple cases and, in general, it converges to it in the limit of the peridynamic horizon going to zero. We solve test problems and compare results with analytical solutions of the classical model or with other numerical solutions. Convergence to the classical solutions is seen in the limit of the horizon going to zero. We then solve the problem of transient heat flow in a plate in which insulated cracks grow and intersect thus changing the heat flow patterns. We also model heat transfer in a fiber-reinforced composite and observe transient but steep thermal gradients at the interfaces between the highly conductive fibers and the low conductivity matrix. Such thermal gradients can lead to delamination cracks in composites from thermal fatigue. The formulation may be used to, for example, evaluate effective thermal conductivities in bodies with an evolving distribution of insulating or permeable, possibly intersecting, cracks of arbitrary shapes.

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“…Peridynamics has been successfully applied to crack propagation [8,12], investigating impact on a brittle solid [22], failure analyses of composites [2,11] and nanotube reinforced composites [9]. The first peridynamic formulation that most researchers have applied from the literature is the "bond-based" model.…”

Section: Introductionmentioning

confidence: 99%

A morphing approach to couple state-based peridynamics with classical continuum mechanics

Han

Lubineau

Azdoud

et al. 2016

Computer Methods in Applied Mechanics and Engineering

140

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Please cite this article as: F. Han, G. Lubineau, Y. Azdoud, A. Askari, A morphing approach to couple state-based peridynamics with classical continuum mechanics, Comput. Methods Appl. Mech. Engrg. (2015), http://dx.doi. org/10.1016/j.cma.2015.12.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractA local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

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Studies of dynamic crack propagation and crack branching with peridynamics

Cited by 616 publications

References 30 publications

Multiscale modeling and simulation of rolling contact fatigue

Multiscale modeling and simulation of rolling contact fatigue

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

A morphing approach to couple state-based peridynamics with classical continuum mechanics

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