Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force

By Jacob Fish, M. Nuggehally, Mark S. Shephard, C. Picu, Santiago Badia, Michael L. Parks, Max D. Gunzburger. 2007

141 citations recorded by the source corpus.

A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain where fine scale features need to be resolved, a continuum sub-domain which can adequately describe the macroscale deformation and an overlap interphase sub-domain that has a blended description of the two. The problem is formulated in terms of equilibrium equations with a blending between the continuum stress and the atomistic force in the interphase. Coupling between the continuum and the atomistics is established by imposing constraints between the continuum solution and the atomistic solution over the interphase sub-domain in a weak sense. Specifically, in the examples considered here, the atomistic domain is modeled by the aluminum embedded atom method (EAM) inter-atomic potential developed by Ercolessi and Adams [F. Ercolessi, J.B. Adams, Interatomic potentials from first-principles calculations: the force-matching method, Europhys. Lett. 26 (1994) 583] and the continuum domain is a linear elastic model consistent with the EAM potential. The formulation is subjected to patch tests to demonstrate its ability to represent the constant strain modes and the rigid body modes. Numerical examples are illustrated with comparisons to reference atomistic solution. 2007 Elsevier B.V. All rights reserved.

Subfields: Materials Chemistry, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/87977c99b83fc0bcca24a026acc7b167edc5fbc9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Materials Chemistry

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods (2009, methodology): “The AtC method was presented and analyzed in a series of papers, namely references [4, 5, 19, 35].”
A multiscale quasicontinuum method for dissipative lattice models and discrete networks (2014, methodology): “Moreover, the QC method entirely relies on the microstructural lattice topology, unlike approaches as those of Xiao and Belytschko (2004) and Fish et al. (2007), that need a continuum description in addition to the discrete model.”
A force-based coupling scheme for peridynamics and classical elasticity (2013, methodology): “A special class of methods, in which atomistic and continuum models are coupled together by means of an overlapping or bridging domain, appear under the so-called blending methods [3, 4, 13, 16], bridging domain methods [7, 32, 42], or Arlequin method [5, 8, 9, 29], among others.”
A computational library for multiscale modeling of material failure (2013, methodology): “…scale method (BSM) [105,135], composite grid atomistic continuum method (CACM) [33]} or force based {ﬁnite-element/atomistics (FEAt) [63], Coupled atomistics and discrete dislocation (CADD) [118,119], hybrid simulation method (HSM) [75], concurrent AtC coupling (AtC) [39,12]} 2.”