Nanoindentation and incipient plasticity

This paper presents a large-scale atomic resolution simulation of nanoindentation into a thin aluminum film using the recently introduced quasicontinuum method. The purpose of the simulation was to study the initial stages of plastic deformation under the action of an indenter. Two different crystallographic orientations of the film and two different indenter geometries (a rectangular prism and a cylinder) were studied. We obtained both macroscopic load versus indentation depth curves, as well as microscopic quantities, such as the Peierls stress and density of geometrically necessary dislocations beneath the indenter. In addition, we obtain detailed information regarding the atomistic mechanisms responsible for the macroscopic curves. A strong dependence on geometry and orientation is observed. Two different microscopic mechanisms are observed to accommodate the applied loading: (i) nucleation and subsequent propagation into the bulk of edge dislocation dipoles and (ii) deformation twinning

Beyond Kinetic Relations

We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relations explicit one needs to integrate the system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description containing now an internal time scale is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region.Comment: Revised version, 33 pages, 9 figure

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

Hybrid continuum mechanics and atomistic methods for simulating materials deformation and failure

Many aspects of materials deformation and failure are controlled by atomic-scale phenomena that can be explored using molecular statics and molecular dynamics simulations. However, many of these phenomena involve processes on multiple length scales with the result that full molecular statics/molecular dynamics simulations of the entire system are too large to be tractable. In this review, we discuss hybrid models that perform molecular statics/molecular dynamics simulations "without all the atoms," aimed at retaining atomistic detail at a fraction of the computational cost. These methods couple a fully atomistic model in critical regions to regions described by less-expensive continuum methods where they can provide an adequate representation of the important physics. We give an overview of the challenges such models present, with a focus on recent work to address issues of dynamics and finite (non-zero) temperature

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

Umbrella spherical integration: A stable meshless method for non-linear solids

A stable meshless method for studying the finite deformation of non-linear three-dimensional (3D) solids is presented. The method is based on a variational framework with the necessary integrals evaluated through nodal integration. The method is truly meshless, requiring no 3D meshing or tessellation of any form. A local least-squares approximation about each node is used to obtain necessary deformation gradients. The use of a local field approximation makes automatic grid refinement and the application of boundary conditions straightforward. Stabilization is achieved through the use of special 'umbrella' shape functions that have discontinuous derivatives at the nodes. Novel efficient algorithms for constructing the nodal stars and computing the nodal volumes are presented. The method is applied to four test problems: uniaxial tension, simple shear and bending of a bar, and cylindrical indentation. Convergence studies at infinitesimal strain show that the method is well-behaved and converges with the number of nodes for both uniform and non-uniform grids. Typical of meshless methods employing nodal integration, the total energy can be underestimated due to the approximate integration. At finite deformation the method reproduces known exact solutions. The bending example demonstrates an interesting example of torsional buckling resulting from the bending. Copyrigh