Dislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

We study sub-critical fracture driven by thermally activated crack nucleation in the framework of a fiber bundle model. Based on analytic calculations and computer simulations we show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect, i.e. the average lifetime of the system decreases as a power law of the system size, where the exponent depends on the external load and on the temperature. We propose a modified form of the Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the micro-level, thermal fluctuations trigger bursts of breaking events which form a stochastic time series as the system evolves towards failure. Numerical and analytical calculations revealed that both the size of bursts and the waiting times between consecutive events have power law distributions, however, the exponents depend on the load and temperature. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the acceleration of the rupture process close to failure is the consequence of damage localization.

Quasi-continuum (QC) methods are computational techniques, which reduce the complexity of atomistic simulations in a static setting while keeping information on small-scale structures and effects. The main idea is to couple atomistic and continuum models and thus to obtain quite detailed but still not too expensive numerical simulations.

We aim at a mathematically rigorous verification of QC methods by means of discrete to continuum limits. In this article we present our first results for the so-called quasi-nonlocal QC method in the context of fracture mechanics. To this end we start from a one-dimensional chain of atoms with nearest and next-to-nearest neighbour interactions of Lennard-Jones type. This is considered as a fully atomistic model of which the Γ-limits (of zeroth and first order) for an infinite number of atoms are known [7].

The QC models we construct are equal to this fully atomistic model in the atomistic region; in the continuum regime we approximate the next-to-nearest neighbour interactions by some nearest neighbour potential which is related to the so-called Cauchy-Born rule. Further we choose certain representative atoms in order to coarsen the mesh in the continuum region. It turns out that the selection of the representative atoms is crucial and influences the Γ-limits.

We regard a QC model as good if the Γ-limits of zeroth and first order or at least their minimal values and minimizers are the same as those of the fully atomistic model. Our analysis shows that, while in an elastic regime only the size of the atomistic region matters, in the case of fracture a proper choice of the representative atoms is an essential ingredient.

We consider the modeling and simulation of multiscale phenomena which arise in finding the optimal shape design of microcellular composite materials with heterogeneous microstructures. The paper focuses on the solution of the resulting partial differential equation (PDE) constrained structural optimization problem and development of efficient multiscale numerical algorithms which are challenging tools in reducing the computational complexity. The modeling strategy is applied in materials science for microstructural ceramic materials of multiple constituents. Our multiscale method is based on the efficient combination of both macroscopic and microscopic models. The homogenization technique based on the concept of strong separation of scales and the asymptotic expansion of the unknown displacements is applied to extract the macroscopic information from the microscale model.

In the framework of all-at-once approach we find a proper combination of the iterative procedure for the nonlinear problem arising from the first order necessary optimality conditions, also known as Karush-Kuhn-Tucker (KKT) conditions, and efficient large-scale solvers for the stress-strain constitutive equation. We use the path-following predictor-corrector schemes by means of Newton's method and fast multigrid (MG) solution techniques. The performance of two preconditioners, incomplete Cholesky (IC) and algebraic multigrid (AMG), for the resulting homogenized state equation is studied. The comparative analysis for both preconditioners in terms of number of iterations and computing times is presented and discussed. Our interests focus on the parallel implementation of the preconditioning techniques and the use of BoomerAMG as a part of the free software library Hypre developed at the Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory (LLNL).

The work presented is devoted to study the mechanisms and kinetics of plastic deformation of bcc and fcc metals and alloys under shock-wave loading (strain rates > 105 s-1). To study the behavior of metals under conditions described the two scale approach is developed. It comprises molecular dynamics (MD) calculations of dislocation mobility and dislocations nucleation rate and continuum mechanics model with equations for description of elastoplastic deformation, kinetics and dynamics of dislocations.

Dislocation velocities as functions of applied shear stress are calculated from MD in a wide temperature range up to the melting point. Velocity-dependent drag coefficient is introduced to approximate the data obtained.

The influence of Guinier–Preston (GP) zones on dislocation motion is analyzed. The results obtained are used to evaluate temperature dependence of dynamic flow stress and the evolution of dislocations subsystem under shock loading. Data on the attenuation of the elastic precursor and rare surface velocity profiles calculated for Al are in good agreement with the experiments. Simulation of the free surface velocity profiles during shock-wave loading of AlCu alloys is carried out.

In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macroscopic physical quantity, will be appropriately determined from molecular dynamics simulations on the microscale. This way, performance predictions become possible prior to material synthesis. However, standard methods produce in general wrong results for ensemble setups which correspond to battery or capacitor applications.

We introduce a novel method to derive correct values also for such problems. These values are then used in a macroscopic system of partial differential equation (Poisson-Nernst-Planck system) for the numerical simulation of ion migration in a battery.

In the current study an elasto-plastic phase field (PF) model, based on the PF microelasticity theory proposed by A.G. Khachaturyan, is used to investigate the effects of external stresses on the evolution of martensitic microstructure in a Fe-0.3%C polycrystalline alloy. The current model is improved to include the effects of grain boundaries in a polycrystalline material. The evolution of plastic deformation is governed by using a time dependent Ginzburg-Landau equation, solving for the minimization of the shear strain energy. PF simulations are performed in 2D and 3D to study the effects of tension, compression and shear on the martensitic transformation. It has been found that external stresses cause an increase in the volume fraction of the martensitic phase if they add to the net effect of the transformation strains, and cause a decrease otherwise. It has been concluded that the stress distribution and the evolution of martensitic microstructure can be predicted with the current model in a polycrystalline material under applied stresses.

Proteins are complex, yet elegant, machines fine-tuned by evolution to properly fulfill a variety of tasks in the crowded cellular environment. These are, however, very challenging numerically due to their dimension, number of degrees of freedom and the wide range of relevant time scales. With aging, some proteins misfold and form harmful amyloid aggregates associated with multiple neurodegenerative diseases, and in particular Alzheimer’s, which challenge our society today. Here, I present the coarse-grained OPEP (Optimized Potential for Efficient peptide structure Prediction) force field and what we can learn from OPEP simulations to get insights into the self-assembly of amyloid peptides.

Using large-scale, all-atom molecular dynamics simulations, we show that microscopic mechanisms found for molecules on the material surface of siloxane polymers can explain an important surface-hydrophobicity restoration process. In particular, a net orientation and polarization on the surface can be found which is the result of an augmented motion of certain molecules. Based on this result, surface hydrophobicity, its loss through oxidation, and its restoration through a unique interaction between cyclomethicone molecules, oxidized methyl groups, and counterions can be understood.

Dielectric materials with GDR (e.g. CaCu3Ti4O12 – CCTO and isostructural systems, co-doped NiO etc) attract major research interest due to their bright prospective in energy storage and memory devices. However, after years of intensive experimental and theoretical studies of GDR materials, physical nature of their extremely high complex dielectric permittivity (specifically, real part ∼ 104 - 106) is still not established convincingly. Another serious problem is excessively high imaginary part of the permittivity (which usually exceeds real one). Better understanding on physical mechanisms and limitations of GDR behavior in aforementioned dielectrics could be achieved based on polaronic phase transition criteria, proposed S. Fratini and P. Quémerais [Eur. Phys. Journ. B14, 99 (2000)]. In particular, ‘melting’ of Polaronic Wigner Crystal (PWC) either to ‘polaronic liquid’ or ‘electron liquid’ manifests two different scenarios of PWC phase transition at increment of concentrations of appropriate dopants. The former scenario is certainly preferable for ionic dielectrics with GDR behavior, while the latter one would yield in metal-like dielectric response with very high real permittivity, but unacceptable loss. Described approach provides physically transparent guidelines for selection of prospective host dielectrics with GDR behavior and quantitative estimations on critical dopant/polaron concentrations, corresponding to both aforementioned types of the phase transitions as well as temperature ranges suitable for GDR.

First principle calculations were performed to evaluate stress effect on the diffusion process of oxygen vacancy in ZrO2 film, and oxidation rate of Zr was evaluated by solving simple diffusion equations. Our calculation results have indicated that both the vacancy formation and migration energies of ZrO2 increase with increasing compressive applied stress. The energy increase causes a decrease in the diffusion coefficient of oxygen vacancy in ZrO2, leading to a decrease in oxidation rate of Zr. The stress effect on diffusion process may explain the experimental fact that Zr is oxidized in proportion to the cubic root of time.

Cluster dynamics (CD) modeling has been used to estimate the long-term evolution of point defect (PD) clusters. However, previous studies have often simplified the governing equations by assuming the maximum size of mobile self-interstitial atom (SIA) clusters and by ignoring the one-dimensional (1D) reaction kinetics of SIA loops. They have also conducted parameter fittings, such as the clustered fraction and the maximum size of clusters produced by collision cascade, to reproduce experimental data. In this study, in addition to modeling the 1D motion of SIA loops in the framework of the production bias model (PBM), reaction rates associated with carbon impurity atoms present in alpha iron were formulated to consider the trapping effect of one-dimensionally migrating SIA loops by a vacancy-carbon (V-C) complex that was shown to have strong bindings with SIA loops by previous atomistic simulations. Calculations results for neutron-irradiated alpha iron showed that the developed CD model can successfully reproduce the saturation trend of the number density of immobile SIA loops in contrast to the prediction using a model without the trapping effect.

The phase-field crystal (PFC) method has emerged as a promising technique to simulate the evolution of crystalline patterns with atomistic resolution on mesoscopic time scales. We use a 2D PFC model based on Elder et al. [Phy. Rev. B 75, 064107 (2007)] to perform a systematic analysis of a liquid-solid interface for a binary alloy system. We propose the method of determining interfacial energies for a curved liquid-solid interface by stabilizing the circular solid seed in the surrounding liquid phase and the liquid droplet in the solid phase for various seed sizes in a finite system. We also investigate the impact of model parameters on the resulting interface energies. The interface energies are computed with various system sizes in order to study the system size effects. In particular, we compare the simulation results in the form of the interface energy as a function of radius with the existing theories.

Results of finite element analysis of linked two and three scale levels tasks are presented. Fields of components of stress concentration tensor function for several models of unit cells of textile composite materials are presented too. Comparison of experimental and computational results of obtained effective properties was carried out and results of this research are introduced. The basis of this phenomenological approaches was made by Prof. N.S. Bahvalov and Prof. B.E. Pobedriya in 80's and finally this method was renovated by Prof. Yu.I. Dimitrienko at Bauman Moscow State Technical University at «Computational mathematics and mathematical physics» department. Computational procedures and program implementation was made using object-oriented design and C/C++ language by A.P. Sokolov. All computational results have been performed using new-developed distributed high-perfomance software system GCD. Multiscale homogenization method was applied for single macroscopic level of composite construction and several connected microscopic levels. The task of stress-strain determination of composite construction was stated automatically by means of automatically defined plan based on certain computational problems. Architecture of software system and finite-element subsystem were developed too. Several practically important tasks were solved and some of its results are attached.

Formation of domain structures in two-step phase separation in Fe-based Fe-Ni-Al alloys are investigated by applying a time-dependent Ginzburg-Landau (TDGL) model. The present authors recently developed a TDGL formulation for ordering processes of B2 and D03 in binary alloys, taking into account the symmetrical relationships between these ordered phases. In this formulation, multiple types of variants of the structures are represented by three order parameters which can be measured independently through crystal structure factors. Mean-field free energies are defined in a form of Landau type expansion with the order parameters and a composition parameter. Interfacial energies due to local variations of degrees of order and composition are given in a gradient square approximation. Kinetic equations for time-evolution of the order parameters and the composition one are derived from the Ginzburg-Landau type potential consisting of the mean-field free energies and the interfacial energy terms. On the other hand, coauthors have investigated domain structures in two-step phase separation of Fe-based Fe-Ni-Al alloys. The evolution of three-dimensional domain structures and composition profiles has been analyzed by electron tomography imaging and energy-dispersive X-ray spectroscopy. In this work the authors performed three-dimensional numerical simulations assuming the thermal processing. The results of the simulations well reproduced the characteristics of the micro-structures obtained from the observations.

Multiscale dislocation dynamics plasticity (MDDP) model is used to investigate the evolution of dislocation microstructure in copper single crystals subjected to low cycle fatigue loading. Half cycle total plastic strain simulations are carried out at strain amplitudes ranging from 1×10-3 to 8×10-3. The initial hardening is investigated and the micro-structural cause behind it is presented. In addition, the loading history is presented and the effect of the initial micro-structure and dislocation distribution on the hardening behavior is studied. In addition, the evolution of the microstructures is examined. In depth analyses of the dislocation microstructures show that: 1) dislocation planes that are parallel and very close to each other are formed, 2) these walls contain dipoles that keep on zipping and unzipping during the first few cycles until they reach some stable zipping configuration. We can see that the hardening rate decreases with the increase of the number of cycles where we have large hardening rate in the first cycles then we reach to somehow constant stress. Our results are qualitatively in good agreement with recent experimental results of low cycle fatigue deformation.

Large scale molecular-dynamics simulations of plane shock loading in SiC are performed to reveal the interplay between shock-induced compaction, structural phase transformation (SPT) and plastic deformation. The shock profile is calculated for a wide range of particle velocity from 0.1 km/s to 6.0 km/s. Single crystalline models indicate no induced plasticity or SPT for shock loading below 2.0 km/s. For intermediate particle velocity, between 2.0 km/s and 4.5 km/s the generated shock wave splits into an elastic precursor and a zinc blende to rocksalt structural transformation wave. That is induced by the increase in shock pressure to over 90 GPa and results in a steep increase of density from 3.21 g/cm3 to ∼4.65 g/cm3. For particle velocity greater than 4.5 km/s a single overdriven transformation shock wave is generated. These simulation results provide an atomistic view of the dynamic effects of shock impact on single crystal high-strength ceramics.

In this paper, the Lattice Statics formalism is used to perform Monte Carlo simulations of alloy microstructures when elastic effects are present. It provides sets of long-range effective pair interactions (EPIs), defined in a rigid average reference state, that allow us to compute microstructural evolutions on diffusion time scale. A wide composition range is investigated in order to characterize the different precipitation processes with elasticity (nucleation and growth, spinodal decomposition). An advantage of the approach is to include the concentration dependence of both the effective chemical interactions and the elastic properties of the reference state. The importance of this point is illustrated by comparing the precipitation sequences in two alloys with symmetric average concentrations.

In this paper, we developed a microscopic approach to understand rubber reinforcement using coarse-grained molecular dynamics simulations. We investigated static uniaxial tensile behavior of filled and unfilled rubber models, and found two reinforcement mechanisms. One of these is the same as the mechanism predicted by Guth, which depends only on the volume content of fillers. We have confirmed this mechanism at small strain region. The other is caused by filler-filler network created by the advantage of chemical bond at large strain. In this region, some polymers linked fillers and were stretched, that is, these polymers generated tension. Additionally, we investigated the effect of filler distribution on rubber reinforcement.