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1
Johansson, Petter, Andreas Carlson, and Berk Hess. "Water–substrate physico-chemistry in wetting dynamics." Journal of Fluid Mechanics 781 (September 28, 2015): 695–711. http://dx.doi.org/10.1017/jfm.2015.517.
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We consider the wetting of water droplets on substrates with different chemical composition and molecular spacing, but with an identical equilibrium contact angle. A combined approach of large-scale molecular dynamics simulations and a continuum phase field model allows us to identify and quantify the influence of the microscopic physics at the contact line on the macroscopic droplet dynamics. We show that the substrate physico-chemistry, in particular hydrogen bonding, can significantly alter the flow. Since the material parameters are systematically derived from the atomistic simulations, our continuum model has only one adjustable parameter, which appears as a friction factor at the contact line. The continuum model approaches the atomistic wetting rate only when we adjust this contact line friction factor. However, the flow appears to be qualitatively different when comparing the atomistic and continuum models, highlighting that non-trivial continuum effects can come into play near the interface of the wetting front.
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Hudson, Thomas, Patrick van Meurs, and Mark Peletier. "Atomistic origins of continuum dislocation dynamics." Mathematical Models and Methods in Applied Sciences 30, no. 13 (December 15, 2020): 2557–618. http://dx.doi.org/10.1142/s0218202520500505.
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This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.
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RAHMAN, R., and A. HAQUE. "A PERIDYNAMICS FORMULATION BASED HIERARCHICAL MULTISCALE MODELING APPROACH BETWEEN CONTINUUM SCALE AND ATOMISTIC SCALE." International Journal of Computational Materials Science and Engineering 01, no. 03 (September 2012): 1250029. http://dx.doi.org/10.1142/s2047684112500297.
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In this paper, a multiscale modeling framework has been established between peridynamics and atomistic models. Peridynamics (PD) formulation is based on continuum theory implying nonlocal force based interactions. Peridynamics (PD) and molecular dynamics (MD) have similarities since both use nonlocal force based interaction. It means continuum points in PD and MD atoms are separated by finite distance and exert force upon each other. In this work PD based continuum model of epoxy polymer is defined by meshless Lagrangian particles. MD is coupled with PD based continuum model through a hierarchical multiscale modeling framework. In this framework, PD particles at coarse scale interact with fine scale PD particles by transferring pressure, displacements and velocities among each other. Based on the same hierarchical coupling method, fine scale PD model is seamlessly interfaced with molecular model through an intermediate mesoscale region i.e. coarse-grain atomic model. At the end of this hierarchical downscaling, the information — such as deformation, energy and other important parameters — were captured in the atomistic region under the applied force at micro and macro regions. A two-dimensional plate of neat epoxy was considered for demonstration of such multiscale simulation platform. The region of interest in the 2D plate was interfaced with atomistic model by applying the proposed hierarchical coupling method. The results show reasonable consistency between PD and MD simulations.
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Mikeš, Karel, and Milan Jirásek. "Quasicontinuum Simulation of Nanotextile Based on the Microplane Model." Key Engineering Materials 714 (September 2016): 143–47. http://dx.doi.org/10.4028/www.scientific.net/kem.714.143.
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The quasicontinuum (QC) method is a relatively new computational technique, which combines fast continuum and exact atomistic approaches. The key idea of QC is to reduce the computational cost by reducing degrees of freedom of the fully atomistic approach. In this work, a material model based on the idea of microplanes is used to realize the QC simplification. A formulation convenient for numerical simulation of materials with the structure similar to nanotextile is proposed. The relations between microscopic and macroscopic parameters are derived. Numerical tests show that the proposed model can reach a significant reduction of computational cost for the price of an acceptable error.
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Farafonov, Vladimir, Alexander Lebed, and Nikolay Mchedlov-Petrossyan. "CONTINUUM ELECTROSTATICS INVESTIGATION OF IONIC MICELLES USING ATOMISTIC MODELS." Ukrainian Chemistry Journal 87, no. 6 (July 26, 2021): 55–69. http://dx.doi.org/10.33609/2708-129x.87.06.2021.55-69.
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The key parameter related to the structure of the electric double layer of ionic surfactant micelles – electrostatic potential – is considered. A brief overview of experimental methods and theoretical models for estimating electrostatic potential- is given. The calculating method for the electrostatic potential based on a numerical solution of the Poisson-Boltzmann equation using an atomistic model of anionic surfactant micelle - is proposed. The parameters necessary for the construction of atomistic models - are obtained from molecular dynamic modeling. The electrostatic potentials for the micelles of sodium dodecyl sulfate and cetyltrimethylammonium bromide at different ionic strengths - were calculated by this method. The results are discussed in comparison with the values calculated in the simplified model, the Ohshima – Healy – White equation.
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Huang, Dan, Mengwei Wang, and Guangda Lu. "Continuum Fracture Analysis and Molecular Dynamic Study on Crack Initiation and Propagation in Nanofilms." Journal of Nanomaterials 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/732434.
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Crack initiation and propagation in a nanostructured nickel film were studied by molecular dynamic simulation as well as an interatomic-potential-based continuum approach. In the molecular dynamic simulation, the interatomic potential was described by using Embedded Atom Method (EAM), and a reduced 2D plane model was employed to simulate the mechanical behavior of nanofilms. Atomistic simulation shows that the reduced plane model in this paper can not only reveal the physical nature of crack initiation clearly but also give the critical time of crack initiation accurately as the continuum fracture analysis does. The normal stress and average atom energy at the crack tip which resulted from atomistic simulation at the time of crack initiation agree well with the analytical results. On the other hand, the crack propagation in nanofilms was studied by interatomic-potential-based continuum fracture mechanics analysis based on Griffith criterion. The coupled continuum-atomic analysis can predict the crack initiation and atomic stress accurately. Continuum analysis with material property parameters determined by interatomic potential is proved to be another promising way of solving failure problem on nanoscale.
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Ghorai, Amitava. "A Review of some Theoretical Models for Point Defect Calculations." Defect and Diffusion Forum 329 (July 2012): 81–0. http://dx.doi.org/10.4028/www.scientific.net/ddf.329.81.
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A Brief Sketch of Different Models for the Calculation of Defect Parameters in Metals and Alloys, Comparison of Data and Limitations Has Been Reviewed here; Especially Relaxations due to a Vacancy Type of Point Defect, its Formation, Migration, Activation Energies and Related other Parameters Based upon the Present Experimental Status. the Models Reviewed Are the Bond Model, Continuum Model, Semi-Discrete Model, Jellium Model, Thermodynamic Model, Lattice Statics Model, Atomistic Continuum Model and Pseudopotential Model. the Main Thrust Concerns the Last Model. the Taylor, Vashishta and Singwi, Harrison, Kleinmann and King and Kutler Form of Exchange and Correlation Function Are Almost Similar, Give Moderate Results and May Be Trusted for Better Results.
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Español, Malena I., Dmitry Golovaty, and J. Patrick Wilber. "Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (January 2018): 20170612. http://dx.doi.org/10.1098/rspa.2017.0612.
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In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.
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Kumari, Sweta, Sri Sadgun Reddy Pulagam, and Amlan Dutta. "Nucleation of Twinning Dislocation Loop in Pt: A Computational Approach." International Journal of Innovative Research in Physics 3, no. 1 (October 4, 2021): 11–18. http://dx.doi.org/10.15864/ijiip.3102.
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Twinning plays a critical part in the plastic deformation of the materials and the strengthening mechanisms and is hence considered as one of the most prevalent deformation mechanisms in metals. Because to the high stacking fault energy of the fcc metals like Al, Pd, and Pt, the extended dislocations are believed to be energetically favored over isolated partials, thereby rendering deformation twinning unfeasible. Nevertheless, some recent experimental researches have confirmed a potential deformation twinning pathway in nanocrystalline platinum. This alternate-shear mechanism has a much lower energy barrier than the usual layer-by-layer twinning. We utilize computations involving atomistic calculations and continuum modeling in this study to examine the genesis of deformation twins in Pt. Atomistic simulations provides the generalized planer fault energy using an EAM (embedded-atom-model) potential. Moreover, a potential energy-based method, namely; a nudged-elastic band (chain of states) has been used to compute the activation energy barrier for the nucleation of the twinning dislocation loop in the alternate-shear model. The critical stress needed for the nucleation of the twinning dislocation loop in platinum is estimated using some of the parameters acquired from atomistic calculations and using them as fitting parameters in the continuum model. The minimum-energy path between the two end states can be identified using this methodology. Through the unusual alternate-shear approach, the results provide a rudimentary but essential dislocationbased perspective of the occurrence of deformation twins in fcc metals.
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Chen, Ching, Sergey Galitskiy, Avanish Mishra, and Avinash M. Dongare. "Modeling laser interactions with aluminum and tantalum targets using a hybrid atomistic-continuum model." Journal of Applied Physics 133, no. 10 (March 14, 2023): 105901. http://dx.doi.org/10.1063/5.0138389.
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A hybrid atomistic-continuum method can model the microstructure evolution of metals subjected to laser irradiation. This method combines classical molecular dynamics (MD) simulations with the two-temperature model (TTM) to account for the laser energy absorption and heat diffusion behavior. Accurate prediction of the temperature evolution in the combined MD-TTM method requires reliable accuracy in electron heat capacity, electron thermal conductivity, and electron–phonon coupling factor across the temperatures generated. This study uses the electronic density of states (DOS) obtained from first-principle calculations. The calculated electron temperature-dependent parameters are used in MD-TTM simulations to study the laser metal interactions in FCC and BCC metals and the phenomenon of laser shock loading and melting. This study uses FCC Al and BCC Ta as model systems to demonstrate this capability. When subjected to short pulsed laser shocks, the dynamic failure behavior predicted using temperature-dependent parameters is compared with the experimentally reported single-crystal and nanocrystalline Al and Ta systems. The MD-TTM simulations also investigate laser ablation and melting behavior of Ta to compare with the ablation threshold reported experimentally. This manuscript demonstrates that integrating the temperature-dependent parameters into MD-TTM simulations leads to the accurate modeling of the laser–metal interaction and allows the prediction of the kinetics of the solid–liquid interface.
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Buehler, Markus J. "Atomistic and continuum modeling of mechanical properties of collagen: Elasticity, fracture, and self-assembly." Journal of Materials Research 21, no. 8 (August 1, 2006): 1947–61. http://dx.doi.org/10.1557/jmr.2006.0236.
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We report studies of the mechanical properties of tropocollagen molecules under different types of mechanical loading including tension, compression, shear, and bending. Our modeling yields predictions of the fracture strength of single tropocollagen molecules and polypeptides, and also allows for quantification of the interactions between tropocollagen molecules. Atomistic modeling predicts a persistence length of tropocollagen molecules ξ ≈ 23.4 nm, close to experimental measurements. Our studies suggest that to describe large-strain or hyperelastic properties, it is critical to include a correct description of the bond behavior and breaking processes at large bond stretch, information that stems from the quantum chemical details of bonding. We use full atomistic calculations to derive parameters for a mesoscopic bead-spring model of tropocollagen molecules. We demonstrate that the mesoscopic model enables one to study the finite temperature, long-time scale behavior of tropocollagen fibers, illustrating the dynamics of solvated tropocollagen molecules for different molecular lengths.
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Grigoriev, F. V., V. B. Sulimov, and A. V. Tikhonravov. "Combined Modeling of the Optical Anisotropy of Porous Thin Films." Coatings 10, no. 6 (May 28, 2020): 517. http://dx.doi.org/10.3390/coatings10060517.
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In this article, a combined approach for studying the optical anisotropy of porous thin films obtained by the glancing angle deposition is presented. This approach combines modeling on the atomistic and continuum levels. First, thin films clusters are obtained using the full-atomistic molecular dynamics simulation of the deposition process. Then, these clusters are represented as a medium with anisotropic pores, the shapes parameters of which are determined using the Monte Carlo based method. The difference in the main components of the refractive index is calculated in the framework of the anisotropic Bruggeman effective medium theory. The presented approach is tested and validated by comparing the analytical and simulation results for the model problems, and then is applied to silicon dioxide thin films. It is found that the maximum difference between the main components of the refractive index is 0.035 in a film deposited at an angle of 80°. The simulation results agree with the experimental data reported in the literature.
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Chen, Yanyan, Xudong Guo, Guojun Zhang, Yang Cao, Dili Shen, Xiaoke Li, Shengfei Zhang, and Wuyi Ming. "Development of a Hybrid Intelligent Process Model for Micro-Electro Discharge Machining Using the TTM-MDS and Gaussian Process Regression." Micromachines 13, no. 6 (May 28, 2022): 845. http://dx.doi.org/10.3390/mi13060845.
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This paper proposed a hybrid intelligent process model, based on a hybrid model combining the two-temperature model (TTM) and molecular dynamics simulation (MDS) (TTM-MDS). Combined atomistic-continuum modeling of short-pulse laser melting and disintegration of metal films [Physical Review B, 68, (064114):1–22.], and Gaussian process regression (GPR), for micro-electrical discharge machining (micro-EDM) were also used. A model of single-spark micro-EDM process has been constructed based on TTM-MDS model to predict the removed depth (RD) and material removal rate (MRR). Then, a GPR model was proposed to establish the relationship between input process parameters (energy area density and pulse-on duration) and the process responses (RD and MRR) for micro-EDM machining. The GPR model was trained, tested, and tuned using the data generated from the numerical simulations. Through the GPR model, it was found that micro-EDM process responses can be accurately predicted for the chosen process conditions. Therefore, the hybrid intelligent model proposed in this paper can be used for a micro-EDM process to predict the performance.
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Rampino, Sergio, Mirco Zerbetto, and Antonino Polimeno. "Stochastic Modelling of 13C NMR Spin Relaxation Experiments in Oligosaccharides." Molecules 26, no. 9 (April 21, 2021): 2418. http://dx.doi.org/10.3390/molecules26092418.
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A framework for the stochastic description of relaxation processes in flexible macromolecules including dissipative effects has been recently introduced, starting from an atomistic view, describing the joint relaxation of internal coordinates and global degrees of freedom, and depending on parameters recoverable from classic force fields (energetics) and medium modelling at the continuum level (friction tensors). The new approach provides a rational context for the interpretation of magnetic resonance relaxation experiments. In its simplest formulation, the semi-flexible Brownian (SFB) model has been until now shown to reproduce correctly correlation functions and spectral densities related to orientational properties obtained by direct molecular dynamics simulations of peptides. Here, for the first time, we applied directly the SFB approach to the practical evaluation of high-quality 13C nuclear magnetic resonance relaxation parameters, T1 and T2, and the heteronuclear NOE of several oligosaccharides, which were previously interpreted on the basis of refined ad hoc modelling. The calculated NMR relaxation parameters were in agreement with the experimental data, showing that this general approach can be applied to diverse classes of molecular systems, with the minimal usage of adjustable parameters.
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Latz, Arnulf, and Jochen Zausch. "Multiscale modeling of lithium ion batteries: thermal aspects." Beilstein Journal of Nanotechnology 6 (April 20, 2015): 987–1007. http://dx.doi.org/10.3762/bjnano.6.102.
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The thermal behavior of lithium ion batteries has a huge impact on their lifetime and the initiation of degradation processes. The development of hot spots or large local overpotentials leading, e.g., to lithium metal deposition depends on material properties as well as on the nano- und microstructure of the electrodes. In recent years a theoretical structure emerges, which opens the possibility to establish a systematic modeling strategy from atomistic to continuum scale to capture and couple the relevant phenomena on each scale. We outline the building blocks for such a systematic approach and discuss in detail a rigorous approach for the continuum scale based on rational thermodynamics and homogenization theories. Our focus is on the development of a systematic thermodynamically consistent theory for thermal phenomena in batteries at the microstructure scale and at the cell scale. We discuss the importance of carefully defining the continuum fields for being able to compare seemingly different phenomenological theories and for obtaining rules to determine unknown parameters of the theory by experiments or lower-scale theories. The resulting continuum models for the microscopic and the cell scale are numerically solved in full 3D resolution. The complex very localized distributions of heat sources in a microstructure of a battery and the problems of mapping these localized sources on an averaged porous electrode model are discussed by comparing the detailed 3D microstructure-resolved simulations of the heat distribution with the result of the upscaled porous electrode model. It is shown, that not all heat sources that exist on the microstructure scale are represented in the averaged theory due to subtle cancellation effects of interface and bulk heat sources. Nevertheless, we find that in special cases the averaged thermal behavior can be captured very well by porous electrode theory.
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Gröger, Roman, and Turab Lookman. "Influence of Dislocations on the Spatial Variation of Microstructure in Martensites." Key Engineering Materials 465 (January 2011): 77–80. http://dx.doi.org/10.4028/www.scientific.net/kem.465.77.
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The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the “strength” of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.
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Ramasubramaniam, A., and V. B. Shenoy. "Growth and Ordering of Si-Ge Quantum Dots on Strain Patterned Substrates." Journal of Engineering Materials and Technology 127, no. 4 (January 30, 2005): 434–43. http://dx.doi.org/10.1115/1.1924559.
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Manipulating the strain distribution along the surface of a substrate has been shown experimentally to promote spatial ordering of self-assembled nanostructures in heteroepitaxial film growth without having to resort to expensive nanolithographic techniques. We present here numerical studies of three-dimensional modeling of self-assembly in Si-Ge systems with the aim of understanding the effect of spatially varying mismatch strain-fields on the growth and ordering of quantum dots. We use a continuum model based on the underlying physics of crystallographic surface steps in our calculations. Using appropriate parameters from atomistic studies, the (100) orientation is found to be unstable under compressive strain; the surface energy now develops a new minimum at an orientation that may be interpreted as the (105) facet observed in SiGe∕Si systems. This form of surface energy allows for the nucleationless growth of quantum dots which start off via a surface instability as shallow stepped mounds whose sidewalls evolve continuously toward their low-energy orientations. The interaction of the surface instability with one- and two-dimensional strain modulations is considered in detail as a function of the growth rate. One-dimensional strain modulations lead to the formation of rows of dots in regions of low mismatch—there is some ordering within these rows owing to elastic interactions between dots but this is found to depend strongly upon the kinetics of the growth process. Two-dimensional strain modulations are found to provide excellent ordering within the island array, the growth kinetics being less influential in this case. For purposes of comparison, we also consider self-assembly of dots for an isotropic surface energy. While the results do not differ significantly from those for the anisotropic surface energy with the two-dimensional strain variation, the one-dimensional strain variation produces profoundly different behavior. The surface instability is seen to start off initially as stripes in regions of low mismatch. However, since stripes are less effective at relaxing the mismatch strain they eventually break up into islands. The spacing of these islands is determined by the wavelength of the fastest growing mode of the Asaro-Tiller-Grinfeld instability. However, the fact that such a growth mode is not observed experimentally indicates the importance of accounting for surface energy anisotropy in growth models.
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Selimov, Alex, Kevin Chu, and David L. McDowell. "Coarse-grained atomistic modeling of dislocations and generalized crystal plasticity." Journal of Micromechanics and Molecular Physics, April 6, 2022, 1–23. http://dx.doi.org/10.1142/s2424913021420133.
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Recent developments in generalized continuum modeling methods ranging from coarse-grained atomistics to micromorphic theory offer potential to make more intimate physical contact with dislocation field problems framed at length scales on the order of microns. We explore a range of discrete dynamical and continuum mechanics approaches to crystal plasticity that are relevant to modeling behavior of populations of dislocations. Predictive atomistic and coarse-grained atomistic models are limited in terms of length and time scales that can be accessed; examples of the latter are discussed in terms of interactions of multiple dislocations in heterogeneous systems. Generalized continuum models alleviate restrictions to a significant extent in modeling larger scales of dislocation configurations and reactions, and are useful to consider effects of dislocation configuration on strength at characteristic length scales of sub-micron and above; these models require a combination of bottomup models and top-down experimental information to inform parameters and model form. The concurrent atomistic-continuum (CAC) method is extended to model complex multicomponent alloy systems using an average atom approach. Examples of CAC are presented, along with potential to assist in informing parameters of a recently developed micropolar crystal plasticity model based on a set of sub-micron dislocation field problems. Prospects for further developments are discussed.
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Marqués, Luis A., Lourdes Pelaz, Iván Santos, Pedro López, and María Aboy. "Atomistic Simulation Techniques in Front-End Processing." MRS Proceedings 1070 (2008). http://dx.doi.org/10.1557/proc-1070-e06-01.
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ABSTRACTAtomistic process models are beginning to play an important role as direct simulation approaches for front-end processes and materials, and also as a pathway to improve continuum modeling. Detailed insight into the underlying physics usingab-initiomethods and classical molecular dynamics simulations will be needed for understanding the kinetics of reduced thermal budget processes and the role of impurities. However, the limited sizes and time scales accessible for detailed atomistic techniques usually lead to the difficult task of relating the information obtained from simulations to experimental data. The solution consists of the use of a hierarchical simulation scheme: more fundamental techniques are employed to extract parameters and models that are then feed into less detailed simulators which allow direct comparison with experiments. This scheme will be illustrated with the atomistic modeling of the ion-beam induced amorphization and recrystallization of silicon. The model is based on the bond defect or IV pair, which is used as the building block of the amorphous phase. It is shown that the recombination of this defect depends on the surrounding bond defects, which accounts for the cooperative nature of the amorphization and recrystallization processes. The implementation of this model in a kinetic Monte Carlo code allows extracting data directly comparable with experiments.
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Ganesan, Hariprasath, Ingo Scheider, and Christian J. Cyron. "Quantifying the High-Temperature Separation Behavior of Lamellar Interfaces in γ-Titanium Aluminide Under Tensile Loading by Molecular Dynamics." Frontiers in Materials 7 (January 14, 2021). http://dx.doi.org/10.3389/fmats.2020.602567.
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γ-titanium aluminide (TiAl) alloys with fully lamellar microstructure possess excellent properties for high-temperature applications. Such fully lamellar microstructure has interfaces at different length scales. The separation behavior of the lamellae at these interfaces is crucial for the mechanical properties of the whole material. Unfortunately, quantifying it by experiments is difficult. Therefore, we use molecular dynamics (MD) simulations to this end. Specifically, we study the high-temperature separation behavior under tensile loading of the four different kinds of lamellar interfaces appearing in TiAl, namely, the γ/α2, γ/γPT, γ/γTT, and γ/γRB interfaces. In our simulations, we use two different atomistic interface models, a defect-free (Type-1) model and a model with preexisting voids (Type-2). Clearly, the latter is more physical but studying the former also helps to understand the role of defects. Our simulation results show that among the four interfaces studied, the γ/α2 interface possesses the highest yield strength, followed by the γ/γPT, γ/γTT, and γ/γRB interfaces. For Type-1 models, our simulations reveal failure at the interface for all γ/γ interfaces but not for the γ/α2 interface. By contrast, for Type-2 models, we observe for all the four interfaces failure at the interface. Our atomistic simulations provide important data to define the parameters of traction–separation laws and cohesive zone models, which can be used in the framework of continuum mechanical modeling of TiAl. Temperature-dependent model parameters were identified, and the complete traction–separation behavior was established, in which interface elasticity, interface plasticity, and interface damage could be distinguished. By carefully eliminating the contribution of bulk deformation from the interface behavior, we were able to quantify the contribution of interface plasticity and interface damage, which can also be related to the dislocation evolution and void nucleation in the atomistic simulations.
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De Domenico, Dario, Harm Askes, and Elias C. Aifantis. "Capturing wave dispersion in heterogeneous and microstructured materials through a three-length-scale gradient elasticity formulation." Journal of the Mechanical Behavior of Materials 27, no. 5-6 (November 6, 2018). http://dx.doi.org/10.1515/jmbm-2018-2002.
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AbstractLong-range interactions occurring in heterogeneous materials are responsible for the dispersive character of wave propagation. To capture these experimental phenomena without resorting to molecular and/or atomistic models, generalized continuum theories can be conveniently used. In this framework, this paper presents a three-length-scale gradient elasticity formulation whereby the standard equations of elasticity are enhanced with one additional strain gradient and two additional inertia gradients to describe wave dispersion in microstructured materials. It is well known that continualization of lattice systems with distributed microstructure leads to gradient models. Building on these insights, the proposed gradient formulation is derived by continualization of the response of a non-local lattice model with two-neighbor interactions. A similar model was previously proposed in the literature for a two-length-scale gradient formulation, but it did not include all the terms of the expansions that contributed to the response at the same order. By correcting these inconsistencies, the three-length-scale parameters can be linked to geometrical and mechanical properties of the material microstructure. Finally, the ability of the gradient formulation to simulate wave dispersion in a broad range of materials (aluminum, bismuth, nickel, concrete, mortar) is scrutinized against experimental observations.