An embedded statistical method for coupling molecular dynamics and finite element analyses

Abstract

SUMMARYThe coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full threedimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

An Overview of Innovative Strategies for Fracture Mechanics at NASA Langley Research Center

“…Because of the extreme computational cost of interrogating large volumes of materials with atomistic simulation, both concurrent and sequential multiscale methods are being developed. The concurrent multiscale methods are developed to dramatically improve computational efficiency by virtually embedding a small (several million atom) atomistic simulation within a large finite element model 26 , whereas the sequential multiscale methods recast the results of the atomistic simulations for use in continuum-based methods 27 . Recently, a number of atomistic simulation studies on intergranular and transgranular crack propagation in aluminum have been published [27][28][29][30][31] .…”

“…The recently developed embedded statistical coupling method (ESCM) 26 for concurrent multiscale modeling was used. Studying the crack tip nucleation process at different crack orientations and loads revealed the existence of a transition stress intensity, K IT , below which the crack emits full dislocations, and above which deformation twinning becomes dominant.…”

New Developments in the Embedded Statistical Coupling Method: Atomistic/Continuum Crack Propagation

“…The problem of coupling the dynamic response of the MD domain to the static response of the FEM system is discussed in detail in Saether, et al 13 While the dynamic coupling in the ESCM approach cannot be fully achieved without the use of a dynamic FEM simulation, the iterative scheme of coupling, in which the FEM state is continuously updated in accordance with the reported MD displacements, appears to be sufficient to reproduce the evolution of systems with relatively slow dynamics.…”

“…With the use of statistical averages to couple the two computational schemes, the developed approach constitutes a statistical coupling approach, and the developed MD-FEM coupling method is referred to as the embedded statistical coupling method (ESCM). 12,13 The resulting model that consists of an MD system embedded in a FEM domain is depicted in Figure 1.…”

A Continuum-Atomistic Analysis of Transgranular Crack Propagation in Aluminum

“…A recently developed embedded statistical coupling method (ESCM) 6,7 for concurrent multiscale modeling is used. The approach is based on the construction of a coupled atomistic-continuum model.…”