Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model

Kohlhoff, S.; Gumbsch, Peter; Fischmeister, H. F.

doi:10.1080/01418619108213953

Cited by 433 publications

(268 citation statements)

References 18 publications

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“…There exist different concurrent coupling methods such as finite element atomistics method (FEAt) [50], quasicontinuum method (QC) [46,47], coupling of length scales (CLS) [36] [49]. It should be noted that in both cases, the introduction of coarser elements leads to distinct dispersion relations and spectral decompositions atomistic and discrete dislocation (CADD) [48], bridging scale method (BSM) [51] and bridging domain method (BDM) [49].…”

Section: Multiscale Coupling Applied To Contactmentioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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Limitations of single scale approaches to study the complex physics involved in friction have motivated the development of multiscale models. We review the state-of-the-art multiscale models that have been developed up to date. These have been successfully applied to a variety of physical problems, but that were limited, in most cases, to zero Kelvin studies. We illustrate some of the technical challenges involved with simulating a frictional sliding problem, which by nature generates a large amount of heat. These challenges can be overcome by a proper usage of spatial filters, which we combine to a direct finite-temperature multiscale approach coupling molecular dynamics with finite elements. The basic building block relies on the proper definition of a scale transfer operator using the least square minimization and spatial filtering. Then, the restitution force from the generalized Langevin equation is modified to perform a two-way thermal coupling between the two models. Numerical examples are shown to illustrate the proposed coupling formulation.

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Section: Multiscale Coupling Applied To Contactmentioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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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%

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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“…By contrast, force-based coupling mechanisms [4,16,15,31] are comparatively simple in their formulation and, more importantly, they do not suffer from the interfacial consistency errors exhibited by most energybased methods [5,23]. The force-based quasicontinuum (QCF) method [4] is a prototypical example of a force-based atomistic/continuum hybrid method and is the focus of the present paper.…”

Section: Introductionmentioning

confidence: 99%

“…While atomistic models are needed to provide accurate descriptions of defects they are usually too expensive computationally to allow sufficiently large-scale simulations that resolve the elastic far-field, which can, instead, be modelled efficiently by a coarse-grained continuum model. Methodologies for coupling the two different material descriptions were first described in [16,15,24,31]; more recent examples are [1,11,32,14,28]. The numerical analysis of atomistic/continuum hybrid methods is a topic of active research [4, 5, 8, 9, 11, 12, 17-19, 23, 25, 26].…”

Section: Introductionmentioning

confidence: 99%

A priori error analysis of two force-based atomistic/continuum models of a periodic chain

2011

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A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Abstract The force-based quasicontinuum (QCF) approximation is a nonconservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain, that is valid for an arbitrary interaction range, large deformations, and takes coarse-graining into account. Our main tool in this analysis is a new concept of atomistic stress.Moreover, we formulate a new atomistic/continuum coupling mechanism based on coupling stresses instead of forces and extend the a priori analysis to this new method. We show that the new method has several theoretical advantages over the original QCF method.

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Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model

Cited by 433 publications

References 18 publications

MD/FE Multiscale Modeling of Contact

MD/FE Multiscale Modeling of Contact

Multiscale Modeling of Point and Line Defects in Cubic Lattices

A priori error analysis of two force-based atomistic/continuum models of a periodic chain

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