Bridging cell multiscale modeling of fatigue crack growth in fcc crystals

Iacobellis, Vincent; Behdinan, Kamran

doi:10.1002/nme.4968

Cited by 9 publications

(3 citation statements)

References 44 publications

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“…where B D @ @A is the hardening force. Substituting this equation together with Equation (29) into the plastic dissipation (28), it leads to the following expression: If the process is elastic, both L p and P A vanish and the plastic dissipation is zero. This leads to the following definition for † in the intermediate configuration:…”

Section: Plasticity Model At Atomistic Levelmentioning

confidence: 99%

“…In their model, the inter-grain sliding was initiated because of stress concentration near the crack tip that leads to the generation of edge dislocations. Iacobellis and Behdinan [28] employed the bridging cell technique for modeling coupled continuum/atomistic systems at finite temperature to model the fatigue crack growth in single crystal nickel under two crystal orientations at different temperatures, in which a temperature-dependent embedded atom method was proposed for finite temperature simulations.…”

Section: Introductionmentioning

confidence: 99%

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Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit

Khoei

Jahanshahi

2016

Numerical Meth Engineering

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1181has attracted much attention toward computational techniques in scientific research communities. The multi-scale modeling of materials in nanoscale, such as carbon nanotubes [1], nano-wires [2,3], thin films [4], bone structures [5,6], and biological materials [7] is an obvious sign of this attraction. Among the various numerical methods used in computational nano-mechanics, the finite element method (FEM) [8], the molecular dynamics [9], and the multi-scale analysis [10] can be mentioned as the most popular techniques. The constitutive model used in FEM and multi-scale methods is usually based on the Cauchy-Born (CB) hypothesis, which is well documented by Park and Liu [11].Because of the size of nanostructures, the ratio of surface area to volume is large and therefore makes the stresses in surface atoms be a couple of magnitudes larger than the atoms in the bulk of the material. This effect, known as the surface effect, is a property of nanostructures. Basically, the surface effect can be attributed to the difference in chemical bonds at the surface and the bulk of the structure. Sander [12] illustrated that the difference between atomic bonds is due to the redistribution of electric charge produced by the reduced atomic coordination in the surface of the structure. A large number of analytical and computational models have been proposed in the literature to study the surface effects in nanostructures. Analytical models are generally based on the definition of a surface-dependent constitutive formulation for continua. The augmented continuum theory by Gurtin and Murdoch [13,14] introduces the concept of surface elasticity tensor into the conventional theory of elasticity. The surface CB model by Park et al. [15] is based on the decomposition of total potential energy of the system into bulk and surface parts that was used to simulate metallic nanowires [16] and silicon nanostructures [17]. Because the model cannot effectively capture the stresses at corners and surfaces of the structure, the boundary CB model was developed by Qomi et al. [18], employing the surface, edge, and corner elements in addition to the conventional bulk element. The linear interpolation employed in their work requires a large number of quadrature points to be used within the boundary elements. Moreover, the method fails to model arbitrary boundary conditions. In order to circumvent the aforementioned deficiencies, Khoei et al. [19] developed the modified boundary CB method that benefits from a local regression in the vicinity of quadrature points, called the radial quadrature method. The method eliminates the necessity to use large number of Gauss points, and it is applicable to arbitrary boundary conditions.The behavior of nanostructures in transition to plastic limit has been studied by Sunyk et al. [20,21]. They employed the relaxation method proposed by Tadmor et al. [22] to capture the plastic phenomena. In their study, additional degrees of freedom were introduced when the material becomes unstable because of the loss of r...

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Section: Plasticity Model At Atomistic Levelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit

Khoei

Jahanshahi

2016

Numerical Meth Engineering

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“…The aim of this study was to obtain a better understanding of the sapphire's mechanical response in the presence of nanoscale defects using multiscale modeling. This study incorporates the BCM multiscale technique which implements an FE framework throughout the domain making the continuum and atomistic domains couple seamlessly. The transition domain is defined with bridging cells containing both atoms and nodes, through which the displacements of atoms are mapped to the nodes.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of the Nanodefects and Temperature Effect on the Mechanical Response of Sapphire

2016

Self Cite

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A multiscale approach using Bridging Cell Method (BCM) is applied to simulate the combined effect of temperature and alumina's common structural nanodefects such as nanovoids, precracks, and Mg impurities on the mechanical response of single crystal C-plane and M-plane sapphire. The BCM model consists of three domains of continuum, bridging, and atomistic, where the whole system is solved in a finite element (FE) framework. Interatomic interaction potentials and temperaturedependent formulations are incorporated in the atomistic domain to conduct simulations for structures containing nanodefects at a range of finite temperatures from 300 to 1600 K. The results are compared for each case to analyze the effect of temperature and nanodefects. Mechanical response of the material is presented and discussed with respect to ultimate tensile strength (UTS), stress distribution and elasticity. Results show different material behavior for C-plane and M-plane under the same biaxial loading conditions but containing different nanodefects. Precracks are found to be the most critical defects for both systems, which significantly reduce structural strength. J ournalcontinuum domain boundary and V k , A k , and t k are volume, area, and traction of element k, respectively.Having E c calculated, the stiffness of the continuum domain, K c , could be obtained as:

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Multiscale Methods for Lightweight Structure and Material Characterization

Iacobellis

Behdinan

2021

Advanced Multifunctional Lightweight Aerostructures; Design, Development, and Implementation

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Bridging cell multiscale modeling of fatigue crack growth in fcc crystals

Cited by 9 publications

References 44 publications

Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit

Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit

Multiscale Modeling of the Nanodefects and Temperature Effect on the Mechanical Response of Sapphire

Multiscale Methods for Lightweight Structure and Material Characterization

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