A New Method for Coupled Elastic-Atomistic Modelling

Kohlhoff, S.; Schmauder, Siegfried

doi:10.1007/978-1-4684-5703-2_42

Cited by 29 publications

(34 citation statements)

References 15 publications

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“…In one of the earliest works, Kohlhoff and Schmauder [15] and Kohlhoff et al [16] developed a coupled model in which, the finite element analysis was combined with the atomistic model. In this approach, an overlapping domain was defined to enforce the boundary condition on both the atomistic and continuum domains.…”

Section: Introductionmentioning

confidence: 99%

A concurrent multi-scale modeling for dynamic behavior of nano-crystalline structures

Khoei

Aramoon

Jahanbakhshi

et al. 2013

Computational Materials Science

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Section: Introductionmentioning

confidence: 99%

A concurrent multi-scale modeling for dynamic behavior of nano-crystalline structures

Khoei

Aramoon

Jahanbakhshi

et al. 2013

Computational Materials Science

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“…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%

“…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%

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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“…Although this field has acquired a substantial history, it remains an active area of research. Early work by Kohlhoff and collaborators [7,8] created a methodology that combined finite element analysis with atomistic modeling, named FEAt. The FEAt model uses an atomic lattice surrounded by an FE mesh with a limited overlap region that enforces boundary conditions on both atomistic and continuum domains.…”

Section: Introductionmentioning

confidence: 99%

“…Whereas, in a continuum, the free energy is usually the basis for thermoelastic materials since free energy is minimized at equilibrium. 7 Unfortunately, free energy can only be derived from atomistic simulations by complex post-processing based on statistical mechanics. Another issue to consider is what domains in the simulation need atomistic representation and what domains can be represented by continuum and where do they interact: on an interface, over an overlap of finite size or should one region be a (proper) subset the other.…”

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confidence: 99%

A robust, coupled approach for atomistic-continuum simulation.

Aubry¹,

Webb²,

Wagner³

et al. 2004

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This report is a collection of documents written by the group members of the Engineering Sciences Research Foundation (ESRF), Laboratory Directed Research and Development (LDRD) project titled "A Robust, Coupled Approach to Atomistic-Continuum Simulation". Presented in this document is the development of a formulation for performing quasistatic, coupled, atomistic-continuum simulation that includes cross terms in the equilibrium equations that arise due to kinematic coupling and corrections used for the calculation of system potential energy to account for continuum elements that overlap regions containing atomic bonds, evaluations of thermo-mechanical continuum quantities calculated within atomistic simulations including measures of stress, temperature and heat flux, calculation used to determine the appropriate spatial and time averaging necessary to enable these atomisticallydefined expressions to have the same physical meaning as their continuum counterparts, and a formulation to quantify a continuum "temperature field", the first step towards constructing a coupled atomistic-continuum approach capable of finite temperature and dynamic analyses.

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A New Method for Coupled Elastic-Atomistic Modelling

Cited by 29 publications

References 15 publications

A concurrent multi-scale modeling for dynamic behavior of nano-crystalline structures

A concurrent multi-scale modeling for dynamic behavior of nano-crystalline structures

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

A robust, coupled approach for atomistic-continuum simulation.

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