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Designing Ti-6Al-4V microstructure for strain delocalization using neural networks Mater. Theory Pub Date : 2024-03-01 Behnam Ahmadikia, Adolph L. Beyerlein, Jonathan M. Hestroffer, M. Arul Kumar, Irene J. Beyerlein
The deformation behavior of Ti-6Al-4V titanium alloy is significantly influenced by slip localized within crystallographic slip bands. Experimental observations reveal that intense slip bands in Ti-6Al-4V form at strains well below the macroscopic yield strain and may serially propagate across grain boundaries, resulting in long-range localization that percolates through the microstructure. These connected
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Role of interfaces on the mechanical response of accumulative roll bonded nanometallic laminates investigated via dislocation dynamics simulations Mater. Theory Pub Date : 2024-02-27 Aritra Chakraborty, Aaron A. Kohnert, Abigail Hunter, Laurent Capolungo
Unraveling the effects of continuous dislocation interactions with interfaces, particularly at the nanometer length scales, is key to a broader understanding of plasticity, to material design and to material certification. To this end, this work proposes a novel discrete dislocation dynamics-based model for dislocation interface interactions tracking the fate of residual dislocation on interfaces.
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Multiscale modeling of dislocations: combining peridynamics with gradient elasticity Mater. Theory Pub Date : 2024-02-05 Jonas Ritter, Michael Zaiser
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends on boundary conditions on the sample scale. We present a novel approach which is based on a peridynamic dislocation model to deal with the surface boundary value
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Correction: Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases Mater. Theory Pub Date : 2024-01-02 Shuaifang Zhang, Wen Jiang, Michael R. Tonks
Correction: Materials Theory 6: 6 (2022) https://doi.org/10.1186/s41313-021-00037-1 Following publication of the original article [1], the authors identified errors in Fig. 17. The correct figure is given below. The incorrect figure is: The correct figure is: The original article [1] has been corrected. Zhang et al., Assessment of four strain energy decomposition methods for phase field fracture models
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Periodic plane-wave electronic structure calculations on quantum computers Mater. Theory Pub Date : 2023-01-03 Song, Duo, Bauman, Nicholas P., Prawiroatmodjo, Guen, Peng, Bo, Granade, Cassandra, Rosso, Kevin M., Low, Guang Hao, Roetteler, Martin, Kowalski, Karol, Bylaska, Eric J.
A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed, and it was validated using full configuration interaction (FCI) calculations, as well as executions of variational quantum eigensolver (VQE) circuits on Quantinuum’s ion trap quantum computers accessed through Microsoft’s Azure Quantum service
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Relating plasticity to dislocation properties by data analysis: scaling vs. machine learning approaches Mater. Theory Pub Date : 2023-01-03 Hiemer, Stefan, Fan, Haidong, Zaiser, Michael
Plasticity modelling has long relied on phenomenological models based on ad-hoc assumption of constitutive relations, which are then fitted to limited data. Other work is based on the consideration of physical mechanisms which seek to establish a physical foundation of the observed plastic deformation behavior through identification of isolated defect processes (’mechanisms’) which are observed either
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Correction: Constant-depth circuits for dynamic simulations of materials on quantum computers Mater. Theory Pub Date : 2022-11-14 Bassman Oftelie, Lindsay, Van Beeumen, Roel, Younis, Ed, Smith, Ethan, Iancu, Costin, de Jong, Wibe A.
1. Bassman Oftelie et al. Materials Theory (2022) Constant-depth circuits for dynamic simulations of materials on quantum computers (2022) 6:13 DOI: 10.1186/s41313-022-00043-x Download references Authors and Affiliations Lawrence Berkeley National Lab, Berkeley, 94720, CA, USA Lindsay Bassman Oftelie, Roel Van Beeumen, Ed Younis, Costin Iancu & Wibe A. de Jong 2University of California Berkeley, 94720
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Numerical simulations of noisy quantum circuits for computational chemistry Mater. Theory Pub Date : 2022-09-22 Wright, Jerimiah, Gowrishankar, Meenambika, Claudino, Daniel, Lotshaw, Phillip C., Nguyen, Thien, McCaskey, Alexander J., Humble, Travis S.
The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground
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Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science Mater. Theory Pub Date : 2022-05-07 Bauman, Nicholas P., Kowalski, Karol
The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting
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Characterization of dislocation ensembles: measures and complexity Mater. Theory Pub Date : 2022-04-19 Hochrainer, Thomas, Laurson, Lasse, Papanikolaou, Stefanos, Po, Giacomo, Sills, Ryan B.
When dislocations were first proposed at the beginning of the twentieth century to explain basic facts in metallurgy (Orowan 1934; Taylor 1934), the primary hypothesis was that they behave similarly to point particles, forming a liquid at larger scales in analogy to other excitations identified in physics (Anderson 1972). However, as characterization techniques improved, it became clear that dislocations
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Portevin–Le Chatelier effect: modeling the deformation bands and stress-strain curves Mater. Theory Pub Date : 2022-04-11 Mäkinen, Tero, Ovaska, Markus, Laurson, Lasse, Alava, Mikko J.
In the Portevin–Le Chatelier (PLC) effect sample plastic deformation takes place via localized bands. We present a model to account for band dynamics and the variability the bands exhibit. The approach is tuned to account for strain hardening and the strain-rate dependence for the case of so-called type A (propagating) bands. The main experimental features of the fluctuations are a reduction with strain
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Phase field assisted analysis of a solidification based metal refinement process Mater. Theory Pub Date : 2022-03-07 Viardin, A., Böttger, B., Apel, M.
Ultra pure metals have various applications, e. g. as electrical conductors. Crystallization from the melt, e. g. via zone melting, using the segregation of impurities at the solidification front is the basic mechanism behind different technical processes for the refining of metals and semi-metals. In this paper, we focus on a crystallization methodology with a gas cooled tube (“cooled finger”) dipped
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Constant-depth circuits for dynamic simulations of materials on quantum computers Mater. Theory Pub Date : 2022-03-07 Bassman, Lindsay, Van Beeumen, Roel, Younis, Ed, Smith, Ethan, Iancu, Costin, de Jong, Wibe A.
Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth with increasing simulation time for a specific subset
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Phase field simulations of FCC to BCC phase transformation in (Al)CrFeNi medium entropy alloys Mater. Theory Pub Date : 2022-03-07 Zuo, X. J., Coutinho, Y., Chatterjee, S., Moelans, N.
Microstructure simulations for quaternary alloys are still a challenge, although it is of high importance for alloy development. This work presents a Phase field (PF) approach capable of resolving phase transformation in a multicomponent system with a simple and effective way to include the thermodynamic and kinetic information for such a complex system. The microstructure evolution during diffusional
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Prospects of quantum computing for molecular sciences Mater. Theory Pub Date : 2022-03-07 Liu, Hongbin, Low, Guang Hao, Steiger, Damian S., Häner, Thomas, Reiher, Markus, Troyer, Matthias
Molecular science is governed by the dynamics of electrons and atomic nuclei, and by their interactions with electromagnetic fields. A faithful physicochemical understanding of these processes is crucial for the design and synthesis of chemicals and materials of value for our society and economy. Although some problems in this field can be adequately addressed by classical mechanics, many demand an
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Theoretical basis for phase field modeling of polycrystalline grain growth using a spherical-Gaussian-based 5-D computational approach Mater. Theory Pub Date : 2022-03-02 Yeo, Lenissongui C., Costa, Michael N., Bair, Jacob L.
Using a previously developed phase field modeling method, where interface energies are described by spherical gaussians that allow the modeling of complex anisotropies, a new phase field model was developed to model 5-D anisotropy in polycrystalline grain growth. We present the use of quaternions, assigned to individual grains as orientations and misorientations for grain boundaries, as a means of
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Making sense of dislocation correlations Mater. Theory Pub Date : 2022-02-22 Hochrainer, Thomas, Weger, Benedikt, Gupta, Satyapriya
Since crystal plasticity is the result of moving and interacting dislocations, it seems self-evident that continuum plasticity should in principle be derivable as a statistical continuum theory of dislocations, though in practice we are still far from doing so. One key to any statistical continuum theory of interacting particles is the consideration of spatial correlations. However, because dislocations
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Phase-field simulations of fission gas bubble growth and interconnection in U-(Pu)-Zr nuclear fuel Mater. Theory Pub Date : 2022-01-28 Aagesen, Larry K., Casagranda, Albert, Matthews, Christopher, Beeler, Benjamin W., Novascone, Stephen
The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection
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Modeling mesoscale fission gas behavior in UO2 by directly coupling the phase field method to spatially resolved cluster dynamics Mater. Theory Pub Date : 2022-01-27 Kim, Dong-Uk, Blondel, Sophie, Bernholdt, David E., Roth, Philip, Kong, Fande, Andersson, David, Tonks, Michael R., Wirth, Brian D.
Fission gas release within uranium dioxide nuclear fuel occurs as gas atoms diffuse through grains and arrive at grain boundary (GB) bubbles; these GB bubbles grow and interconnect with grain edge bubbles; and grain edge tunnels grow and connect to free surfaces. In this study, a hybrid multi-scale/multi-physics simulation approach is presented to investigate these mechanisms of fission gas release
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Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases Mater. Theory Pub Date : 2022-01-12 Zhang, Shuaifang, Jiang, Wen, Tonks, Michael R.
Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance
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Machine learning-assisted high-throughput exploration of interface energy space in multi-phase-field model with CALPHAD potential Mater. Theory Pub Date : 2022-01-06 Attari, Vahid, Arroyave, Raymundo
Computational methods are increasingly being incorporated into the exploitation of microstructure–property relationships for microstructure-sensitive design of materials. In the present work, we propose non-intrusive materials informatics methods for the high-throughput exploration and analysis of a synthetic microstructure space using a machine learning-reinforced multi-phase-field modeling scheme
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Pinning of dislocations in disordered alloys: effects of dislocation orientation Mater. Theory Pub Date : 2022-01-06 Zaiser, Michael, Wu, Ronghai
The current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the alloy as an effective medium containing a random distribution of dilatation and compression centers representing the volumetric misfit of atoms of different species
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Parallel-GPU-accelerated adaptive mesh refinement for three-dimensional phase-field simulation of dendritic growth during solidification of binary alloy Mater. Theory Pub Date : 2022-01-06 Sakane, Shinji, Takaki, Tomohiro, Aoki, Takayuki
In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance. In this study, we perform a three-dimensional dendrite growth
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VQE method: a short survey and recent developments Mater. Theory Pub Date : 2022-01-06 Fedorov, Dmitry A., Peng, Bo, Govind, Niranjan, Alexeev, Yuri
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to
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Sweep-tracing algorithm: in silico slip crystallography and tension-compression asymmetry in BCC metals Mater. Theory Pub Date : 2022-01-06 Bertin, Nicolas, Zepeda-Ruiz, L.A., Bulatov, V.V.
Direct Molecular Dynamics (MD) simulations are being increasingly employed to model dislocation-mediated crystal plasticity with atomic resolution. Thanks to the dislocation extraction algorithm (DXA), dislocation lines can be now accurately detected and positioned in space and their Burgers vector unambiguously identified in silico, while the simulation is being performed. However, DXA extracts static
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Quantum cluster algorithm for data classification Mater. Theory Pub Date : 2021-10-14 Li, Junxu, Kais, Sabre
We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The
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Surface stress calculations for nanoparticles and cavities in aluminum, silicon, and iron: influence of pressure and validity of the Young-Laplace equation Mater. Theory Pub Date : 2021-09-03 Pizzagalli, Laurent, David, Marie-Laure
This study is dedicated to the determination of the surface energy and stress of nanoparticles and cavities in presence of pressure, and to the evaluation of the accuracy of the Young-Laplace equation for these systems. Procedures are proposed to extract those quantities from classical interatomic potentials calculations, carried out for three distinct materials: aluminum, silicon, and iron. Our investigations
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From mechanism-based to data-driven approaches in materials science Mater. Theory Pub Date : 2021-09-01 Hiemer, Stefan, Zapperi, Stefano
A time-honored approach in theoretical materials science revolves around the search for basic mechanisms that should incorporate key feature of the phenomenon under investigation. Recent years have witnessed an explosion across areas of science of a data-driven approach fueled by recent advances in machine learning. Here we provide a brief perspective on the strengths and weaknesses of mechanism based
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Cell structure formation in a two-dimensional density-based dislocation dynamics model Mater. Theory Pub Date : 2021-05-04 Ronghai Wu, Michael Zaiser
Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at
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Slip-free multiplication and complexity of dislocation networks in FCC metals Mater. Theory Pub Date : 2021-03-29 Sh. Akhondzadeh, Nicolas Bertin, Ryan B. Sills, Wei Cai
During plastic deformation of crystalline solids, intricate networks of dislocation lines form and evolve. To capture dislocation density evolution, prominent theories of crystal plasticity assume that 1) multiplication is driven by slip in active slip systems and 2) pair-wise slip system interactions dominate network evolution. In this work, we analyze a massive database of over 100 discrete dislocation
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On the three-dimensional spatial correlations of curved dislocation systems Mater. Theory Pub Date : 2021-03-10 Joseph Pierre Anderson, Anter El-Azab
Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific
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Length scales and scale-free dynamics of dislocations in dense solid solutions Mater. Theory Pub Date : 2020-11-04 Gábor Péterffy, Péter D. Ispánovity, Michael E. Foster, Xiaowang Zhou, Ryan B. Sills
The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe0.70Ni0.11Cr0.19 over a range of stresses and temperatures. These roughness profiles reveal the hallmark features of a depinning transition. Namely, below a temperature-dependent critical stress, the dislocation
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Probing the transition from dislocation jamming to pinning by machine learning Mater. Theory Pub Date : 2020-10-09 Henri Salmenjoki, Lasse Laurson, Mikko J. Alava
Collective motion of dislocations is governed by the obstacles they encounter. In pure crystals, dislocations form complex structures as they become jammed by their anisotropic shear stress fields. On the other hand, introducing disorder to the crystal causes dislocations to pin to these impeding elements and, thus, leads to a competition between dislocation-dislocation and dislocation-disorder interactions
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Symmetry breaking during defect self-organization under irradiation Mater. Theory Pub Date : 2020-05-24 Yongfeng Zhang, Yipeng Gao, Cheng Sun, Daniel Schwen, Chao Jiang, Jian Gan
One of the most intriguing phenomena under radiation is the self-organization of defects, such as the void superlattices, which have been observed in a list of bcc and fcc metals and alloys when the irradiation conditions fall into certain windows defined by temperature and dose rate. A superlattice features a lattice parameter and a crystal structure. Previously, it has been shown that the superlattice
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A Filon-like integration strategy for calculating exact exchange in periodic boundary conditions: a plane-wave DFT implementation Mater. Theory Pub Date : 2020-04-17 Eric J Bylaska, Kevin Waters, Eric D Hermes, Judit Zádor, Kevin M Rosso
An efficient and accurate approach for calculating exact exchange and other two-electron integrals has been developed for periodic electronic structure methods. Traditional approaches used for integrating over the Brillouin zone in band structure calculations, e.g. trapezoidal or Monkhorst-Pack, are not accurate enough for two-electron integrals. This is because their integrands contain multiple singularities
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Mechanics of moving defects in growing sheets: 3-d, small deformation theory Mater. Theory Pub Date : 2020-04-16 Amit Acharya, Shankar C. Venkataramani
Growth and other dynamical processes in soft materials can create novel types of mesoscopic defects including discontinuities for the second and higher derivatives of the deformation, and terminating defects for these discontinuities. These higher-order defects move “easily", and can thus confer a great degree of flexibility to the material. We develop a general continuum mechanical framework from
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Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields Mater. Theory Pub Date : 2020-04-07 Yejun Gu, Jaafar A. El-Awady
A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional discrete dislocation dynamics simulations, continuum dislocation dynamics simulations, or crystal plasticity simulations
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Brittle to quasi-brittle transition and crack initiation precursors in crystals with structural Inhomogeneities Mater. Theory Pub Date : 2019-11-01 S. Papanikolaou, P. Shanthraj, J. Thibault, C. Woodward, F. Roters
Crack initiation emerges due to a combination of elasticity, plasticity, and disorder, and it displays strong dependence on the material’s microstructural details. The characterization of the structural uncertainty in the original microstructure is typically empirical and systematic characterization protocols are lacking. In this paper, we propose an investigational tool in the form of the curvature
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Overdamped langevin dynamics simulations of grain boundary motion Mater. Theory Pub Date : 2019-05-27 Carolina Baruffi, Alphonse Finel, Yann Le Bouar, Brigitte Bacroix, Oguz Umut Salman
Macroscopic properties of structural materials are strongly dependent on their microstructure. However, the modeling of their evolution is a complex task because of the mechanisms involved such as plasticity, recrystallization, and phase transformations, which are common processes taking place in metallic alloys. This complexity led to a growing interest in atomistic simulations formulated without
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The Green tensor of Mindlin’s anisotropic first strain gradient elasticity Mater. Theory Pub Date : 2019-03-15 Giacomo Po, Nikhil Chandra Admal, Markus Lazar
We derive the Green tensor of Mindlin’s anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of triclinic media. In contrast to its classical counterpart, the Green tensor is non-singular at the origin, and it converges to the classical tensor a few characteristic
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GD3: generalized discrete defect dynamics Mater. Theory Pub Date : 2019-01-31 Laurent Capolungo, Vincent Taupin
A mesoscale model is introduced to study the dynamics of material defects lying at interface junctions. The proposed framework couples the dynamics of discrete dislocation and disclination lines. Disclinations are expected to be natural defects at interface junctions; their presence serving the purpose of accommodating discontinuities in rotation fields at material interface junctions. Crystallography-based
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Thermodynamic considerations of same-metal electrodes in an asymmetric cell Mater. Theory Pub Date : 2019-01-25 M. H. Braga, N. S. Grundish, A. J. Murchison, J. B. Goodenough
An electrochemical cell contains three open thermodynamic systems that, in dynamic equilibrium, equalize their electrochemical potentials with that of their surrounding by forming an electric-double-layer-capacitor at the interface of the electrolyte with each of the two electrodes. Since the electrode/electrolyte interfaces are heterojunctions, the electrochemical potentials or Fermi levels of the
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“Irregularization” of systems of conservation laws Mater. Theory Pub Date : 2018-08-15 Hunter Swan, Woosong Choi, Stefanos Papanikolaou, Matthew Bierbaum, Yong S. Chen, James P. Sethna
We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result in defects which are more singular, and we thus refer to such schemes as “irregularizations”. In particular, we seek to produce delta shock defects which satisfy
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Mixed-mode growth of a multicomponent precipitate in the quasi-steady state regime Mater. Theory Pub Date : 2018-05-23 Tohid Naseri, Daniel Larouche, Rémi Martinez, Francis Breton
An exact analytical solution of the Fick’s second law was developed and applied to the mixed-mode growth of a multicomponent ellipsoidal precipitate growing with constant eccentricities in the quasi-stationary regime. The solution is exact if the nominal composition, equilibrium concentrations and material properties are assumed constant, and can be applied to compounds having no limitations in the
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Annihilation and sources in continuum dislocation dynamics Mater. Theory Pub Date : 2018-03-20 Mehran Monavari, Michael Zaiser
Continuum dislocation dynamics (CDD) aims at representing the evolution of systems of curved and connected dislocation lines in terms of density-like field variables. Here we discuss how the processes of dislocation multiplication and annihilation can be described within such a framework. We show that both processes are associated with changes in the volume density of dislocation loops: dislocation
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Determining Cosserat constants of 2D cellular solids from beam models Mater. Theory Pub Date : 2018-01-31 Stefan Liebenstein, Michael Zaiser
We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modeling strategies are used
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An analysis of two classes of phase field models for void growth and coarsening in irradiated crystalline solids Mater. Theory Pub Date : 2018-01-31 K. Ahmed, A. El-Azab
A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also found
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Erratum to: a novel model of third phase inclusions on two phase boundaries Mater. Theory Pub Date : 2017-07-28 Andrew A. Prudil, Michael J. Welland
Upon publication of the original manuscript (Prudil and Welland 2017) discrepancies were highlighted in Eq. (50) [equation (1) here]. The equation in the original manuscript (Prudil and Welland 2017) erroneously included a factor of 2 on theta and read:$$ \cos \left(2\theta \right)=\frac{\sigma_{\alpha \gamma }}{2{\sigma}_{\alpha \beta }} $$(1) This equation should read as below:$$ \cos \left(\theta
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Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations Mater. Theory Pub Date : 2017-07-11 Nikhil Chandra Admal, Giacomo Po, Jaime Marian
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model
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Stability and symmetry of ion-induced surface patterning Mater. Theory Pub Date : 2017-06-21 Christopher S. R. Matthes, Nasr M. Ghoniem, Daniel Walgraef
We present a continuum model of ion-induced surface patterning. The model incorporates the atomic processes of sputtering, re-deposition and surface diffusion, and is shown to display the generic features of the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear and non-linear stability analyses of the evolution equation give estimates of the emerging pattern wavelength and spatial
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Why Materials Theory? Mater. Theory Pub Date : 2017-05-25 Anter El-Azab
Materials science is an interdisciplinary field with the broad objectives of understanding the structure and properties of materials and the discovery of new materials. In his historical account of this field titled The Coming of Materials Science (Cahn et al. 2003), R. W. Cahn referred to the middle of the past century as the time materials science was born out of metallurgy. Materials science has
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Fracture as a material sink Mater. Theory Pub Date : 2017-05-25 K. Y. Volokh
Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be interpreted as the local material sink. Mass conservation is violated locally in the area of material failure. We consider a theoretical formulation of the coupled mass
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A novel model of third phase inclusions on two phase boundaries Mater. Theory Pub Date : 2017-05-25 Andrew A. Prudil, Michael J. Welland
A new computationally efficient model of an included phase located at the interface between two other phases is developed by projecting the boundaries of the inclusion onto the boundary between the two other phases. This reduces the 3D problem to one on a 2D surface while still being embedded in 3D space, which significantly reduces computational expense of solving the system. The resulting model is
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Formulation of strongly non-local, non-isothermal dynamics for heterogeneous solids based on the GENERIC with application to phase-field modeling Mater. Theory Pub Date : 2017-05-25 Markus Hütter, Bob Svendsen
The purpose of the current work is the formulation of models for conservative and non-conservative dynamics in solid systems with the help of the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and Öttinger, Phys. Rev. E 56(6), 6620 (1997); Öttinger and Grmela, Phys. Rev. E 56(6), 6633 (1997)). In this context, the resulting models are inherently spatially