Multiscale coupling using a finite element framework at finite temperature

Iacobellis, Vincent; Behdinan, Kamran

doi:10.1002/nme.4355

Cited by 16 publications

(8 citation statements)

References 62 publications

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“…In the continuum domain, the total energy, E c , can be described as the summation of the energy density of nodes excluding the surface tractions:

E_{normalC} = \sum_{k = 1}^{n_{k}} (\int_{D^{normalC}} W ({normal∇}_{k}) normald V_{k} - \int_{\partial} D^{C} t_{k} \cdot u_{_{normalC}} normald A_{k})

where n k is the number of elements, W is the strain energy obtained from Cauchy–Born rule, ∇ k is the deformation gradient of the k th element, u c is the displacement, ∂D C is the continuum domain boundary and V k , A k , and t k are volume, area, and traction of element k , respectively.…”

Section: Methodsmentioning

confidence: 99%

“…To avoid very short time steps and very high strain rates, a temperature‐dependent potential energy formulation based on the local quasiharmonic approximation is used in BCM. In this approach the free energy of the system is minimized by accounting for the atomistic vibrations about the primary structure.…”

Section: Methodsmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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

2016

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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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“…In the continuum domain, the total energy, E c , can be described as the summation of the energy density of nodes excluding the surface tractions:

E_{normalC} = \sum_{k = 1}^{n_{k}} (\int_{D^{normalC}} W ({normal∇}_{k}) normald V_{k} - \int_{\partial} D^{C} t_{k} \cdot u_{_{normalC}} normald A_{k})

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

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“…The derivation of Equation can be found in . Similarly, the other diagonal stiffness terms in Equation are

{boldK}_{A} = {falsefalse}_{\sum}^{{boldx}_{i}^{(a)} \in {normalΩ}^{A}} {falsefalse}_{\sum}^{{boldx}_{j}^{(a)} \in {normalΩ}^{A}} \frac{\partial^{2} U}{\partial {boldx}_{i}^{(a)} \partial {boldx}_{j}^{(a)}},

{boldK}_{C} = {falsefalse}_{\sum}^{e = 1} \int_{{normalΩ}_{e}^{C}} \frac{\partial {boldF}_{e}^{T}}{\partial x^{(n)}} \frac{\partial^{2} ψ ({boldF}_{e})}{\partial F_{e} \partial {boldF}_{e}} \frac{\partial {boldF}_{e}}{\partial {boldx}^{(n)}} d V_{e} .

…”

Section: Formulationmentioning

confidence: 99%

“…In this paper, the previously developed bridging cell method is extended for the application of modeling fatigue crack growth. With this methodology, each domain in the model is described in a finite element framework, coupling each domain seamlessly together.…”

Section: Introductionmentioning

confidence: 99%

Bridging cell multiscale modeling of fatigue crack growth in fcc crystals

Iacobellis

Behdinan

2015

Int. J. Numer. Meth. Engng

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SUMMARYThe previously developed bridging cell method for modeling coupled continuum/atomistic systems at finite temperature is used to model fatigue crack growth in single crystal nickel under two crystal orientations at different temperatures. The method is expanded to implement a temperature-dependent embedded atom method potential for finite temperature simulations avoiding time-scale restrictions associated with small timesteps. Results for the fatigue simulation were compared with respect to deformation behavior, stress distribution, and crack length. Results showed very different crack growth mechanisms between the two crystal orientations as well as reduced resistance to crack growth with increased temperature.

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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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Multiscale coupling using a finite element framework at finite temperature

Cited by 16 publications

References 62 publications

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

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

Bridging cell multiscale modeling of fatigue crack growth in fcc crystals

Multiscale Methods for Lightweight Structure and Material Characterization

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