Uncertainty quantification (UQ) methods bring rigorous statistical connections to the analysis of computational and experiment data, and provide a basis for probabilistically assessing margins associated with safety and reliability. The DAKOTA toolkit developed at Sandia National Laboratories implements a number of UQ methods, which are being increasingly adopted by modeling and simulation teams to facilitate these analyses. This report disseminates results as to the performance of DAKOTA's stochastic expansion methods for UQ on a representative application. Our results provide a number of insights that may be of interest to future users of these methods, including the behavior of the methods in estimating responses at varying probability levels, and the expansion levels for the methodologies that may be needed to achieve convergence.
This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate energy potential, the atomic J integral we developed is calculable and accurate at finite/room temperatures. In Chapter 6, we return in part to the fundamental efforts to connect material behavior at the atomic scale to that of the continuum. In this chapter, we devise theory that predicts the onset of instability characteristic of fracture/failure via atomic simulation. In Chapters 7 and 8, we describe the culmination of the project in connecting atomic information to continuum modeling. In these chapters we show that cohesive zone models are: (a) derivable from molecular dynamics in a robust and systematic way, and (b) when used in the more efficient continuum-level finite element technique provide results that are comparable and well-correlated with the behavior at the atomic-scale. Moreover, we show that use of these same cohesive zone elements is feasible at scales very much larger than that of the lattice. Finally, in Chapter 9 we describe our work in developing the efficient non-reflecting boundary conditions necessary to perform transient fracture and shock simulation with molecular dynamics.
Understanding charge transport processes at a molecular level using computational techniques is currently hindered by a lack of appropriate models for incorporating anisotropic electric fields, as occur at charged fluid/solid interfaces, in molecular dynamics (MD) simulations. In this work, we develop a model for including electric fields in MD using an atomistic-to-continuum framework. Our model represents the electric potential on a finite element mesh satisfying a Poisson equation with source terms determined by the distribution of the atomic charges. The method is verified using simulations where analytical solutions are known or comparisons can be made to existing techniques. A Calculation of a salt water solution in a silicon nanochannel is performed to demonstrate the method in a target scientific application.
In modeling thermal transport in nanoscale systems, classical molecular dynamics (MD) explicitly represents phonon modes and scattering mechanisms, but electrons and their role in energy transport are missing. Furthermore, the assumption of local equilibrium between ions and electrons often fails at the nanoscale. We have coupled MD (implemented in the LAMMPS MD package) with a partial differential equation based representation of the electrons (implemented using finite elements). The coupling between the subsystems occurs via a local version of the two-temperature model. Key parameters of the model are calculated using the Time Dependent Density Functional Theory with either explicit or implicit energy flow. We will discuss application of this work in the context of the US DOE Center for Integrated Nanotechnologies (CINT).
Performing coupled thermomechanical simulations is becoming an increasingly important aspect of nuclear weapon (NW) safety assessments in abnormal thermal environments. While such capabilities exist in SIERRA, they have thus far been used only in a limited sense to investigate NW safety themes. An important limiting factor is the difficulty associated with developing geometries and meshes appropriate for both thermal and mechanical finite element models, which has limited thermomechanical analysis to simplified configurations. This work addresses the issue of how to perform coupled analyses on models where the underlying geometries and associated meshes are different and tailored to their relevant physics. Such an approach will reduce the model building effort and enable previously developed single-physics models to be leveraged in future coupled simulations. A combined-environment approach is presented in this report using SIERRA tools, with quantitative comparisons made between different options in SIERRA. This report summarizes efforts on running a coupled thermomechanical analysis using the SIERRA Arpeggio code.
Materials with characteristic structures at nanoscale sizes exhibit significantly different mechani-cal responses from those predicted by conventional, macroscopic continuum theory. For example,nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the materialdecreases with decreasing grain size. The origin of this effect is believed to be a change in defor-mation mechanisms from dislocation motion across grains and pileup at grain boundaries at mi-croscopic grain sizes to rotation of grains and deformation within grain boundary interface regionsfor nanostructured materials. These rotational defects are represented by the mathematical conceptof disclinations. The ability to capture these effects within continuum theory, thereby connectingnanoscale materials phenomena and macroscale behavior, has eluded the research community.The goal of our project was to develop a consistent theory to model both the evolution ofdisclinations and their kinetics. Additionally, we sought to develop approaches to extract contin-uum mechanical information from nanoscale structure to verify any developed continuum theorythat includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those thatpossess highly directional bonding within their molecular structures such as liquid crystals, cova-lent ceramics, polymers and biological materials. This level of accuracy is critical for engineeringdesign and thermo-mechanical analysis is performed in micro- and nanosystems. The researchproposed here innovates on how these nanoscale deformation mechanisms should be incorporatedinto a continuum mechanical formulation, and provides the foundation upon which to develop ameans for predicting the performance of advanced engineering materials.4 AcknowledgmentThe authors acknowledge helpful discussions with Farid F. Abraham, Youping Chen, Terry J.Delph, Remi Dingreville, James W. Foulk III, Robert J. Hardy, Richard Lehoucq, Alejandro Mota,Gregory J. Wagner, Edmund B. Webb III and Xiaowang Zhou. Support for this project was pro-vided by the Enabling Predictive Simulation Investment Area of Sandia's Laboratory DirectedResearch and Development (LDRD) program.5
This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.