Ronald E. Miller

Atomistic/continuum coupling in computational materials science

Important advances in multi-scale computer simulation techniques for computational materials science have been made in the last decade as scientists and engineers strive to imbue continuum-based models with more-realistic details at quantum and atomistic scales. One major class of multi-scale models directly couples a region described with full atomistic detail to a surrounding region modelled using continuum concepts and finite element methods. Here, the development of such coupled atomistic/continuum models is reviewed within a single coherent framework with the aim of providing both non-specialists and specialists with insight into the key ideas, features, differences and advantages of prevailing models. Some applications and very recent advances are noted, and important challenges for extending these models to their fullest potential are discussed.

The Quasicontinuum Method: Overview, applications and current directions

The Quasicontinuum (QC) Method, originally conceived and developed by Tadmor, Ortiz and Phillips [1] in 1996, has since seen a great deal of development and application by a number of researchers. The idea of the method is a relatively simple one. With the goal of modeling an atomistic system without explicitly treating every atom in the problem, the QC provides a framework whereby degrees of freedom are judiciously eliminated and force/energy calculations are expedited. This is combined with adaptive model refinement to ensure that full atomistic detail is retained in regions of the problem where it is required while continuum assumptions reduce the computational demand elsewhere. This article provides a review of the method, from its original motivations and formulation to recent improvements and developments. A summary of the important mechanics of materials results that have been obtained using the QC approach is presented. Finally, several related modeling techniques from the literature are briefly discussed. As an accompaniment to this paper, a website designed to serve as a clearinghouse for information on the QC method has been established at www.qcmethod.com. The site includes information on QC research, links to researchers, downloadable QC code and documentation.

A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods

A partitioned-domain multiscale method is a computational framework in which certain key regions are modeled atomistically while most of the domain is treated with an approximate continuum model (such as finite elements). The goal of such methods is to be able to reproduce the results of a fully atomistic simulation at a reduced computational cost. In recent years, a large number of partitioned-domain methods have been proposed. Theoretically, these methods appear very different to each other making comparison difficult. Surprisingly, it turns out that at the implementation level these methods are in fact very similar. In this paper, we present a unified framework in which fourteen leading multiscale methods can be represented as special cases.We use this common framework as a platform to test the accuracy and efficiency of the fourteen methods on a test problem; the structure and motion of a Lomer dislocation dipole in face-centered cubic aluminum. This problem was carefully selected to be sufficiently simple to be quick to simulate and straightforward to analyze, but not so simple to unwittingly hide differences between methods. The analysis enables us to identify generic features in multiscale methods that correlate with either high or low accuracy and either fast or slow performance.All tests were performed using a single unified computer code in which all fourteen methods are implemented. This code is being made available to the public along with this paper.

A coupled atomistic/continuum model of defects in solids

Abstract A method is introduced for reducing the degrees of freedom in simulations of mechanical behavior of materials without sacrificing important physics. The method essentially combines the quasicontinuum (QC) method with continuum defect models such as the discrete dislocation (DD) method. The QC formulation is used to couple a fully atomistic region to a defect-free elastic continuum. Defects existing in the elastic continuum region of the full problem of interest are treated by the DD-like methods with special boundary conditions. The full coupled problem is then solved by an Eshelby-like procedure involving superposition of the QC and DD problems, and is appropriate in both 2d and 3d. Special attention is given to dealing with dislocation defects. A procedure for the “passing” of dislocation defects from the atomistic to the continuum description in 2d problems is also presented. The overall 2d method with dislocation defects is validated by comparing the predictions of the coupled model to “exact” fully atomistic models for several equilibrium dislocation geometries and a nanoindentation problem in aluminum, and excellent agreement is obtained. The method proposed here should find application to a broad host of problems associated with the multiscale modeling of atomistic, nano- and micromechanical behavior of crystalline solids under mechanical loads.

Coupled Atomistic/Discrete Dislocation Simulations of Nanoindentation at Finite Temperature

Simulations of nanoindentation in single crystals are performed using a finite temperature coupled atomistic/continuum discrete dislocation (CADD) method. This computational method for multiscale modeling of plasticity has the ability of treating dislocations as either atomistic or continuum entities within a single computational framework. The finite-temperature approach here inserts a Nose-Hoover thermostat to control the instantaneous fluctuations of temperature inside the atomistic region during the indentation process. The method of thermostatting the atomistic region has a significant role on mitigating the reflected waves from the atomistic/continuum boundary and preventing the region beneath the indenter from overheating. The method captures, at the same time, the atomistic mechanisms and the long-range dislocation effects without the computational cost of full atomistic simulations. The effects of several process variables are investigated, including system temperature and rate of indentation. Results and the deformation mechanisms that occur during a series of indentation simulations are discussed.

Atomistic simulation of nanoindentation into copper multilayers

Atomic-scale simulations are used to examine the plastic behaviour of copper multi-layered thin films during nanoindentation tests. It is found that glide of nucleated dislocation loops and slip in the grain boundaries are the main operating deformation mechanisms in such multi-layered polycrystals. Furthermore, for a very small layer thickness, slip in the grain boundary dominates over the dislocation mediated plasticity. In order to survey the resistance of a multi-layered metal thin film to plastic deformation during nanoindentation, hardness versus penetration depth curves are plotted. Hardness curves reveal softening of multi-layer films, i.e. a reverse Hall–Petch effect is found for layer thicknesses in the nanometre range.

A molecular dynamics study of twin width, grain size and temperature effects on the toughness of 2D-columnar nanotwinned copper

The introduction of twin boundaries (TBs) within nanocrystalline grains has given scientists an opportunity to enhance mechanical properties that are usually mutually exclusive: strength and ductility. This research is focused on developing a complete understanding of the influences of twin width, grain size and temperature on the deformation characteristics and properties of nanotwinned Cu by large-scale molecular dynamics simulations. Simulation results have shown that a materials toughness can be enhanced by introducing nanotwins, and the enhancement is more pronounced for the higher twin density structures and at lower temperatures. Nanotwinned grains are found to be highly anisotropic in their plastic response; ductile along TBs but strong across them. A random polycrystalline sample gains toughness through the combined response of variously oriented grains. At extremely low temperature, toughness values are elevated further due to depressed dislocation activities inside the grains. The study has also revealed that, unlike twin width refinement, grain size refinement may not always yield superior properties, and may deteriorate material toughness.

An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events

Small volume deformation can produce two types of plastic instability events. The first involves dislocation nucleation as a dislocation by dislocation event and occurs in nanoparticles or bulk single crystals deformed by atomic force microscopy or small nanoindenter forces. For the second instability event, this involves larger scale nanocontacts into single crystals or their films wherein multiple dislocations cooperate to form a large displacement excursion or load drop. With dislocation work, surface work, and stored elastic energy, one can account for the energy expended in both single and multiple dislocation events. This leads to an energy balance criterion which can model both the displacement excursion and load drop in either constant load or fixed displacement experiments. Nanoindentation of Fe-3% Si (100) crystals with various oxide film thicknesses supports the proposed approach.

Finite temperature multiscale computational modeling of materials at nanoscale

The A multiscale computational method (CADD) is presented for modeling of materials at nanoscale whereby a continuum region containing defects is coupled to a fully atomistic region. The method reduces the degree of freedom in simulations of mechanical behavior of nanomaterials without sacrificing important physics. Applications to nanoindentation are used to validate and demonstrate the capabilities of the model.

Finite Temperature Coupled Atomistic/Continuum Discrete Dislocation Dynamics Simulation of Nanoindentation

Simulations of nanoindentation in a hexagonal aluminum single crystal are performed using a finite temperature coupled atomistic/continuum discrete dislocation (CADD) method. The method captures, at the same time, the atomistic mechanisms and the long-range effects without the computational cost of full atomistic simulations. The effects of several process variables are investigated, including system temperature. We discuss the results and the deformation mechanisms that occur during a series of indentation simulations.