Simulation of the (001) plane crack in α-iron employing a new boundary scheme

Mullins, Mayes; Dokainish, M. A.

doi:10.1080/01418618208236930

Cited by 112 publications

(72 citation statements)

References 19 publications

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“…As a result, the framework of multiscale/ multiphysics (MSMP) methods has emerged [1][2][3] which, in the area of materials behavior includes two categories, namely, sequential and concurrent. In sequential multiscaling methods [1,2], simulations are performed at a fine/ atomic scale and the fundamental material properties obtained at these scales are used in the coarse scale/ continuum level simulations. In general, fine scale simulations are inherently stochastic, thereby an appropriate quantification of uncertainty associated with material properties requires a large number of simulations, and each simulation is typically by itself computationally demanding.…”

Section: Introductionmentioning

confidence: 99%

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Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Gur

Frantziskonis

2016

Modelling Simul. Mater. Sci. Eng.

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Martensitic phase transformation in NiTi shape memory alloys (SMA) occurs over a hierarchy of spatial scales, as evidenced from observed multiscale patterns of the martensitic phase fraction, which depend on the material microstructure and on the size of the SMA specimen. This paper presents a methodology for the multiscale tracking of the thermally induced martensitic phase transformation process in NiTi SMA. Fine scale stochastic phase field simulations are coupled to macroscale experimental measurements through the compound wavelet matrix method (CWM). A novel process for obtaining CWM fine scale wavelet coefficients is used that enhances the effectiveness of the method in transferring uncertainties from fine to coarse scales, and also ensures the preservation of spatial correlations in the phase fraction pattern. Size effects, well-documented in the literature, play an important role in designing the multiscale tracking methodology. Molecular dynamics (MD) simulations are employed to verify the phase field simulations in terms of different statistical measures and to demonstrate size effects at the nanometer scale. The effects of thermally induced martensite phase fraction uncertainties on the constitutive response of NiTi SMA is demonstrated.

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Section: Introductionmentioning

confidence: 99%

“…Wavelet based methods form a viable concurrent multiscale modeling toolbox [1][2][3][6][7][8][9]. They substantially reduce the computational overhead, without compromising accuracy, required to transfer information from one physical scale to another.…”

Section: Introductionmentioning

confidence: 99%

Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Gur

Frantziskonis

2016

Modelling Simul. Mater. Sci. Eng.

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“…Early work featured one-way [9][10][11][12][13][14] or two-way [15][16][17][18][19] coupled methods, in which displacement fields established at the interface between continuum and atomistic regions were computed either from sophisticated interfacial conditions or from initial conditions derived from continuum elasticity theory. Increases in computing power permitted more realistic two-way couplings, whereby atomistic fields were permitted to affect the far-field elastic continua through the latter's discretization with finite elements [20][21][22][23]. Such improvements in the coupling algorithms enabled description of dynamic crack growth [21].…”

Section: Introductionmentioning

confidence: 99%

“…Although some early work attempted to parameterize stress-strain relationships in the far-field region with atomic potentials [20][21][22], more efficient considerations of selected atomistic effects on material behavior were achieved through the initial developments of the quasicontinuum theory [26][27][28] that employed hyperelastic constitutive behavior, derived from atomistic potentials, for the overlaying finite elements. In the subsequent decade, significant new developments in methodologies have improved the fidelity of atomistically informed, continuum multiscale computational methods [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Point and Line Defects in Cubic Lattices

Chung

Clayton

2007

Int J Mult Comp Eng

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 2008 REPORT TYPE Reprint DATES COVERED (From SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESA reprint from the International Journal for Multiscale Computational Engineering, vol. 5, nos. 3 and 4, pp. 203-226, 2007. 14. ABSTRACT A multilength scale method based on asymptotic expansion homogenization (AEH) is developed to compute minimum energy configurations of ensembles of atoms at the fine length scale and the corresponding mechanical response of the material at the coarse length scale. This multiscale theory explicitly captures heterogeneity in microscopic atomic motion in crystalline materials, attributed, for example, to the presence of various point and line lattice defects. The formulation accounts for large deformations of nominally hyperelastic, monocrystalline solids. Unit cell calculations are performed to determine minimum energy configurations of ensembles of atoms of body-centered cubic tungsten in the presence of periodic arrays of vacancies and screw dislocations of line orientations [111] or [100]. Results of the theory and numerical implementation are verified versus molecular statics calculations based on conjugate gradient minimization (CGM) and are also compared with predictions from the local Cauchy-Born rule. For vacancy defects, the AEH method predicts the lowest system energy among the three methods, while computed energies are comparable between AEH and CGM for screw dislocations. Computed strain energies and defect energies (e.g., energies arising from local internal stresses and strains near defects) are used to construct and evaluate continuum energy functions for defective crystals parameterized via the vacancy density, the dislocation density tensor, and the generally incompatible lattice deformation gradient. For crystals with vacancies, a defect energy increasing linearly with vacancy density and applied elastic deformation is suggested, while for crystals with screw d...

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“…Coupled methods, e.g. multi-scale methods, usually couple atomistic mechanics or quantum theory and classical continuum mechanics [11][12][13]. A comprehensive review of such methods is given in [14,15].…”

Section: Introductionmentioning

confidence: 99%

A coupled distinct lattice spring model for rock failure under dynamic loads

Guo-jie

Khalili

Fang

et al. 2012

Computers and Geotechnics

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a b s t r a c tIt is necessary to take into account the micro discretization of natural rock when studying its macroscopic failure behavior. This requirement has resulted in renewed and increased interest in the discrete or framework/lattice numerical modeling techniques. However, to fully construct a numerical model for practical applications using a discrete numerical model is computationally difficult with current computing technologies. Hence, a coupled model has been developed to overcome this limitation by coupling the Distinct Lattice Spring Model (DLSM) and the Numerical Manifold Method (NMM). In the coupled model, the microscopic discrete model of the rock is represented by a system of discrete particles interacting via springs while the macroscopic level model is represented by the NMM. The proposed model bears a structure of three layers corresponding to the DLSM model, the NMM model, and a model for coupling, respectively. The coupling model is based on a newly developed Particle based Manifold Method (PMM) to bridge the DLSM with the NMM. The proposed coupled model can reduce the computational resources needed for the purely discrete particle based model. This study introduces theoretical aspects of the coupled model together with a few examples to demonstrate its correctness and feasibility.

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Simulation of the (001) plane crack in α-iron employing a new boundary scheme

Cited by 112 publications

References 19 publications

Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Multiscale Modeling of Point and Line Defects in Cubic Lattices

A coupled distinct lattice spring model for rock failure under dynamic loads

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