E. B. Tadmor

University of Minnesota Duluth, Duluth, Minnesota, United States

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Publications (57)132.85 Total impact

  • V Sorkin, R S Elliott, E B Tadmor
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    ABSTRACT: The quasicontinuum (QC) method, in its local (continuum) limit, is applied to materials with a multilattice crystal structure. Cauchy–Born (CB) kinematics, which accounts for the shifts of the crystal motif, is used to relate atomic motions to continuum deformation gradients. To avoid failures of CB kinematics, QC is augmented with a phonon stability analysis that detects lattice period extensions and identifies the minimum required periodic cell size. This approach is referred to as Cascading Cauchy–Born kinematics (CCB). In this paper, the method is described and developed. It is then used, along with an effective interaction potential (EIP) model for shape-memory alloys, to simulate the shape-memory effect and pseudoelasticity in a finite specimen. The results of these simulations show that (i) the CCB methodology is an essential tool that is required in order for QC-type simulations to correctly capture the first-order phase transitions responsible for these material behaviors, and (ii) that the EIP model adopted in this work coupled with the QC/CCB methodology is capable of predicting the characteristic behavior found in shape-memory alloys.
    Modelling and Simulation in Materials Science and Engineering 05/2014; 22(5):055001. DOI:10.1088/0965-0393/22/5/055001 · 1.49 Impact Factor
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    ABSTRACT: Nanostructures are technological devices constructed on a nanometer length scale more than a thousand times thinner than a human hair. Due to the unique properties of matter at this scale, such devices offer great potential for creating novel materials and behaviors that can be leveraged to benefit mankind. This paper addresses a particular challenge involved in the design of nanostructures-their stochastic or apparently random response to external loading. This is because fundamentally the function that relates the energy of a nanostructure to the arrangement of its atoms is extremely nonconvex, with each minimum corresponding to a possible equilibrium state that may be visited as the system responds to loading. Traditional atomistic simulation techniques are not capable of systematically addressing this complexity. Instead, we construct an equilibrium map (EM) for the nanostructure, analogous to a phase diagram for bulk materials, which fully characterizes its response. Using the EM, definitive predictions can be made in limiting cases and the spectrum of responses at any desired loading rate can be obtained. The latter is important because standard atomistic methods are fundamentally limited, by computational feasibility, to simulations of loading rates that are many orders of magnitude faster than reality. In contrast, the EM-based approach makes possible the direct simulation of nanostructure experiments. We demonstrate the method's capabilities and its surprisingly complex results for the case of a nanoslab of nickel under compression.
    Proceedings of the National Academy of Sciences 04/2014; 111(17). DOI:10.1073/pnas.1402029111 · 9.81 Impact Factor
  • Woo Kyun Kim, Ellad B Tadmor
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    ABSTRACT: Dislocations are line defects that play a key role in the plasticity of crystalline materials and affect their thermal, chemical, and electrical properties. Typically dislocations are treated as stable defects; e.g., the equilibrium core structure of a dislocation is obtained by minimizing the crystal potential energy with respect to atom positions. Here we show for the first time the possibility of "entropically stabilized dislocations" that exist due to entropic effects without a corresponding potential energy well. An entropically stabilized dislocation was discovered in an accelerated multiscale quasicontinuum simulation. Its entropic nature was verified with fully atomistic free energy calculations and explained by a simple continuum-based model. This result has important consequences for the study of dislocations as well as for temporal multiscale methods that use information from the potential energy surface to accelerate time in molecular simulations.
    Physical Review Letters 03/2014; 112(10):105501. DOI:10.1103/PhysRevLett.112.105501 · 7.73 Impact Factor
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    ABSTRACT: The quasicontinuum (QC) method is a spatial multiscale method that extends the length scales accessible to fully atomistic simulations (like molecular dynamics (MD)) by several orders of magnitude. While the recent development of the so-called “hot-QC method” enables dynamic simulations at finite temperature, the times accessible to these simulations remain limited to the sub-microsecond time scale due to the small time step required for stability of the numerical integration. To address this limitation, we develop a novel finite-temperature QC method that can treat much longer time scales by coupling the hot-QC method with hyperdynamics—a method for accelerating time in MD simulations. We refer to the new approach as “hyper-QC”. As in the original hyperdynamics method, hyper-QC is targeted at dynamical systems that exhibit a separation of time scales between short atomic vibration periods and long waiting times in metastable states. Acceleration is achieved by modifying the hot-QC potential energy to reduce the energy barriers between metastable states in a manner that ensures that the characteristic dynamics of the system are preserved. First, the high accuracy of hot-QC in reproducing rare event kinetics is demonstrated. Then, the hyper-QC methodology is validated by comparing hyper-QC results with those of hot-QC and full MD for a one-dimensional chain of atoms interacting via a Lennard–Jones potential.
    Journal of the Mechanics and Physics of Solids 02/2014; 63:94–112. DOI:10.1016/j.jmps.2013.10.001 · 4.29 Impact Factor
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    ABSTRACT: This paper discusses the motivation for the creation of cyberinfrastructures to enhance specific technical areas of research. It then goes onto provide a review of two cyberinfrastructures supported by the National Science Foundation, OpenKIM and CAMS, which are geared towards enhancing materials modeling at the atomic scale. Their objectives, accomplishments, and future goals are discussed. Lastly, the future outlook for cyberinfrastructures such as these to impact materials modeling is discussed.
    Current Opinion in Solid State and Materials Science 12/2013; 17(6). DOI:10.1016/j.cossms.2013.10.004 · 7.17 Impact Factor
  • Ye. Hakobyan, E. B. Tadmor, R. D. James
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    ABSTRACT: An objective quasicontinuum (OQC) method is developed for simulating rodlike systems that can be represented as a combination of locally objective structures. An objective structure (OS) is one for which a group of atoms, called a “fundamental domain” (FD), is repeated using specific rules of translation and rotation to build a more complex structure. An objective Cauchy-Born rule defines the kinematics of the OS atoms in terms of a set of symmetry parameters and the positions of the FD atoms. The computational advantage lies in the capability of representing a large system of atoms through a small set of symmetry parameters and FD atom positions. As an illustrative example, we consider the deformation of a copper single-crystal nanobeam which can be described as an OS. OQC simulations are performed for uniform and nonuniform bending for two different orientations (nanobeam axis oriented along [111] and [100]) and compared with elastica results. In the uniform bending case, the [111]-oriented single-crystal nanobeam experiences elongation, while the [100]-oriented nanobeam experiences contraction in total length. The nonuniform bending allows for stretching, contraction, and bending as deformation. Under certain loading conditions, dislocation nucleation is observed within the FD.
    Physical review. B, Condensed matter 12/2012; 86(24). DOI:10.1103/PhysRevB.86.245435 · 3.66 Impact Factor
  • Woo Kyun Kim, Ellad B. Tadmor
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    ABSTRACT: The self-consistent method of lattice dynamics (SCLD) is used to obtain an analytical solution for the free energy of a periodic, one-dimensional, mono-atomic chain accounting for fourth-order anharmonic effects. For nearest-neighbor interactions, a closed-form analytical solution is obtained. In the case where more distant interactions are considered, a system of coupled nonlinear algebraic equations is obtained (as in the standard SCLD method) however with the number of equations dramatically reduced. The analytical SCLD solutions are compared with a numerical evaluation of the exact solution for simple cases and with molecular dynamics simulation results for a large system. The advantages of SCLD over methods based on the harmonic approximation are discussed as well as some limitations of the approach.
    Journal of Statistical Physics 09/2012; 148(5). DOI:10.1007/s10955-012-0559-x · 1.28 Impact Factor
  • Ellad B. Tadmor, Ronald E. Miller, Ryan S. Elliott
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    ABSTRACT: 1. Introduction; 2. Scalars, vectors and tensors; 3. Kinematics of deformation; 4. Mechanical conservation and balance laws; 5. Thermodynamics; 6. Constitutive relations; 7. Boundary-value problems, energy principles and stability; 8. Universal equilibrium solutions; 9. Numerical solutions: the finite element method; 10. Approximate solutions: reduction to the engineering theories; 11. Further reading; Appendices; Index.
    Continuum Mechanics and Thermodynamics 12/2011; DOI:10.1017/CBO9781139017657 · 1.43 Impact Factor
  • Ellad B. Tadmor, Ronald E. Miller
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    ABSTRACT: 1. Introduction; Part I. Continuum Mechanics and Thermodynamics: 2. Essential continuum mechanics and thermodynamics; Part II. Atomistics: 3. Lattices and crystal structures; 4. Quantum mechanics of materials; 5. Empirical atomistic models of materials; 6. Molecular statics; Part III. Atomistic Foundations of Continuum Concepts: 7. Classical equilibrium statistical mechanics; 8. Microscopic expressions for continuum fields; 9. Molecular dynamics; Part IV. Multiscale Methods: 10. What is multiscale modeling?; 11. Atomistic constitutive relations for multilattice crystals; 12. Atomistic/continuum coupling: static methods; 13. Atomistic/continuum coupling: finite temperature and dynamics; Appendix; References; Index.
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    ABSTRACT: Nanoscale modeling of materials often involves the use of molecular simulations or multiscale methods. These approaches frequently use empirical (fitted) interatomic potentials to represent the response of the material. Currently, no standardized approach exists for estimating the accuracy of interatomic potentials. In addition, a lack of standardization in programming interfaces for potentials and the lack of a systematic infrastructure for archiving them makes it difficult to use potentials for new applications and to reproduce published results. The Knowledgebase of Interatomic Models (KIM) (http://openKIM.org) is a 4-year NSF CDI program which attempts to address these limitations. One difficulty in the use of interatomic models is that simulation codes and interatomic potentials are written in a variety of programming languages. In order to allow the programs and model subroutines to be mutually compatible, it is necessary to define a robust application programming interface (API) designed to accommodate the requirements of molecular simulations. The KIM project has developed such an API in collaboration with key members of the molecular simulation community. The API is based on the concept of descriptor files, which define all variables and methods needed for input and output for a given application or model. The API addresses issues such as naming conventions for models (unique names), neighbor-list objects and their interface, system of units, unit conversion, and a complete description of variables and methods. In this talk we will present a brief overview of the KIM framework and then provide details on the KIM API protocol. We invite the molecular simulation community to participate in the KIM project and contribute to the standardization efforts under way.
    2011 AIChE Annual Meeting; 10/2011
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    ABSTRACT: Atomistic simulations in materials science play a key role in realistic scientific and industrial applications. However, the predictive capability of these approaches hinges on the accuracy of the model (potential or force field) used to describe the atomic interactions. Modern models are optimized to reproduce electronic structure results for a dataset of representative atomic configurations. However, no standardized approach currently exists for quantifying the range of applicability of an interatomic model or estimating the accuracy of its predictions. This makes it difficult or even impossible to select an appropriate model for a given application. A second difficulty is that since computer implementations of interatomic models do not subscribe to coding standards, it is hard to connect a given model to a desired simulation tool. This talk will describe a current NSF-CDI funded effort to create an open source online tool that addresses these limitations: the Knowledgebase of Interatomic Models (http://openKIM.org). KIM will allow users to compare model predictions with reference data, to generate new predictions by uploading simulation test codes, and to download models conforming to application programming interface (API) standards which are being developed in collaboration with atomistic simulation community. Inthis talk I will give an overview of the KIM project and describe recent developments.
    2011 AIChE Annual Meeting; 10/2011
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    JOM: the journal of the Minerals, Metals & Materials Society 07/2011; 63(7):17-17. DOI:10.1007/s11837-011-0102-6 · 1.40 Impact Factor
  • Nikhil Chandra Admal, E B Tadmor
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    ABSTRACT: A two-step unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving-Kirkwood procedure to arbitrary multibody potentials. Two ambiguities associated with the original Irving-Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the nonuniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the nonuniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the nonuniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving-Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonly-used microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multibody potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one.
    The Journal of Chemical Physics 05/2011; 134(18):184106. DOI:10.1063/1.3582905 · 3.12 Impact Factor
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    Nikhil Chandra Admal, Ellad B. Tadmor
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    ABSTRACT: The microscopic definition for the Cauchy stress tensor has been examined in the past from many different perspectives. This has led to different expressions for the stress tensor and consequently the "correct" definition has been a subject of debate and controversy. In this work, a unified framework is set up in which all existing definitions can be derived, thus establishing the connections between them. The framework is based on the non-equilibrium statistical mechanics procedure introduced by Irving, Kirkwood and Noll, followed by spatial averaging. The Irving--Kirkwood--Noll procedure is extended to multi-body potentials with continuously differentiable extensions and generalized to non-straight bonds, which may be important for particles with internal structure. Connections between this approach and the direct spatial averaging approach of Murdoch and Hardy are discussed and the Murdoch--Hardy procedure is systematized. Possible sources of non-uniqueness of the stress tensor, resulting separately from both procedures, are identified and addressed. Numerical experiments using molecular dynamics and lattice statics are conducted to examine the behavior of the resulting stress definitions including their convergence with the spatial averaging domain size and their symmetry properties. Comment: 86 pages
    Journal of Elasticity 08/2010; DOI:10.1007/s10659-010-9249-6 · 1.04 Impact Factor
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    M. Arndt, V. Sorkin, E. B. Tadmor
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    ABSTRACT: We discuss algorithms for lattice-based computations, in particular lattice reduction, the detection of nearest neighbors, and the computation of clusters of nearest neighbors. We focus on algorithms that are most efficient for low spatial dimensions (typically d=2,3) and input data within a reasonably limited range. This makes them most useful for physically oriented numerical simulations, for example of crystalline solids. Different solution strategies are discussed, formulated as algorithms, and numerically evaluated.
    Journal of Computational Physics 07/2009; 228(13):4858-4880. DOI:10.1016/j.jcp.2009.03.039 · 2.49 Impact Factor
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    Ronald E Miller, E B Tadmor
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    ABSTRACT: 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.
    Modelling and Simulation in Materials Science and Engineering 05/2009; 17(5):053001. DOI:10.1088/0965-0393/17/5/053001 · 1.49 Impact Factor
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    ABSTRACT: The quasicontinuum (QC) method is applied to materials possessing a multilattice crystal structure. Cauchy-Born (CB) kinematics, which accounts for the shifts of the crystal basis, is used in continuum regions to relate atomic motions to continuum deformation gradients. To avoid failures of the CB kinematics, QC is augmented with a phonon stability analysis that detects lattice period extensions and identifies the minimum required periodic cell size. This augmented approach is referred to as Cascading Cauchy-Born kinematics. The method is analyzed for both first- and second-order phase transformations, and demonstrated numerically on a one-dimensional test problem.
    Journal of Computer-Aided Materials Design 11/2007; 14:219-237. DOI:10.1007/s10820-007-9084-7 · 1.30 Impact Factor
  • L. Kucherov, E. B. Tadmor, R. E. Miller
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    ABSTRACT: 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. Copyright © 2006 John Wiley & Sons, Ltd.
    International Journal for Numerical Methods in Engineering 03/2007; 69(13):2807 - 2847. DOI:10.1002/nme.1871 · 1.96 Impact Factor
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    L Kucherov, E. B. Tadmor
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    ABSTRACT: Twinning is an important deformation mode in hexagonal close-packed (hcp) materials that can strongly affect fracture toughness. In order to clarify the early stages of twin nucleation, lattice statics simulations of zirconium crystals containing mixed-mode basal cracks with ½ 1 2 1 0Š and ½1 1 0 0Š front orientations were carried out using an embedded-atom method potential. The simulations show that crack tip twin nucleation is a two-stage process: (I) initial plastic deformation occurs within a thin layer ahead of the crack, possibly involving basal slip, crack tip blunting by the formation of Frank partials or an hcp-face-centered cubic (fcc) transformation produced by Shockley partials emitted from the crack tip and (II) a twin forms in the surrounding hcp matrix. In this second stage, either a f1 1 2 1g twin is nucleated homogeneously or a f1 0 1 1g twin is nucleated heterogeneously by Shockley partials that nucleate inside the fcc region and penetrate the hcp matrix.
    Acta Materialia 03/2007; 55(6). DOI:10.1016/j.actamat.2006.10.056 · 3.94 Impact Factor

Publication Stats

3k Citations
132.85 Total Impact Points


  • 2007–2014
    • University of Minnesota Duluth
      • Department of Mathematics & Statistics
      Duluth, Minnesota, United States
  • 2012
    • University of Minnesota Twin Cities
      • Department of Aerospace Engineering and Mechanics
      Minneapolis, Minnesota, United States
  • 2000–2007
    • Technion - Israel Institute of Technology
      • Faculty of Mechanical Engineering
      Haifa, Haifa District, Israel
  • 1997–2001
    • Harvard University
      • • School of Engineering and Applied Sciences
      • • Department of Physics
      Cambridge, MA, United States
  • 1996–1999
    • Brown University
      • School of Engineering
      Providence, Rhode Island, United States