Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry, and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.
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Vikram Gavini et al 2023 Modelling Simul. Mater. Sci. Eng. 31 063301
Alexander Stukowski 2010 Modelling Simul. Mater. Sci. Eng. 18 015012
The Open Visualization Tool (OVITO) is a new 3D visualization software designed for post-processing atomistic data obtained from molecular dynamics or Monte Carlo simulations. Unique analysis, editing and animations functions are integrated into its easy-to-use graphical user interface. The software is written in object-oriented C++, controllable via Python scripts and easily extendable through a plug-in interface. It is distributed as open-source software and can be downloaded from the website http://ovito.sourceforge.net/.
Erik van der Giessen et al 2020 Modelling Simul. Mater. Sci. Eng. 28 043001
Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.
S Lucarini et al 2022 Modelling Simul. Mater. Sci. Eng. 30 023002
FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by Moulinec and Suquet for the homogenization of composites. Since then many different approaches have been proposed for a more accurate and efficient resolution of the non-linear homogenization problem. Furthermore, the method has been pushed beyond its original purpose and has been adapted to a variety of problems including conventional and strain gradient plasticity, continuum and discrete dislocation dynamics, multi-scale modeling or homogenization of coupled problems such as fracture or multi-physics problems. In this paper, a comprehensive review of FFT approaches for micromechanical simulations will be made, covering the basic mathematical aspects and a complete description of a selection of approaches which includes the original basic scheme, polarization based methods, Krylov approaches, Fourier–Galerkin and displacement-based methods. Then, one or more examples of the applications of the FFT method in homogenization of composites, polycrystals or porous materials including the simulation of damage and fracture will be presented. The applications will also provide an insight into the versatility of the method through the presentation of existing synergies with experiments or its extension toward dislocation dynamics, multi-physics and multi-scale problems. Finally, the paper will analyze the current limitations of the method and try to analyze the future of the application of FFT approaches in micromechanics.
Simon Gramatte et al 2024 Modelling Simul. Mater. Sci. Eng. 32 045010
In this study, we critically evaluate the performance of various interatomic potentials/force fields against a benchmark ab initio database for bulk amorphous alumina. The interatomic potentials tested in this work include all major fixed charge and variable charge models developed to date for alumina. Additionally, we introduce a novel machine learning interatomic potential constructed using the NequIP framework based on graph neural networks. Our findings reveal that the fixed-charge potential developed by Matsui and coworkers offers the most optimal balance between computational efficiency and agreement with ab initio data for stoichiometric alumina. Such balance cannot be provided by machine learning potentials when comparing performance with Matsui potential on the same computing infrastructure using a single Graphical Processing Unit. For non-stoichiometric alumina, the variable charge potentials, in particular ReaxFF, exhibit an impressive concordance with density functional theory calculations. However, our NequIP potentials trained on a small fraction of the ab initio database easily surpass ReaxFF in terms of both accuracy and computational performance. This is achieved without large overhead in terms of potential fitting and fine-tuning, often associated with the classical potential development process as well as training of standard deep neural network potentials, thus advocating for the use of data-efficient machine learning potentials like NequIP for complex cases of non-stoichiometric amorphous oxides.
John A Mitchell et al 2023 Modelling Simul. Mater. Sci. Eng. 31 055001
SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.
Avik Mahata et al 2018 Modelling Simul. Mater. Sci. Eng. 26 025007
Homogeneous nucleation from aluminum (Al) melt was investigated by million-atom molecular dynamics simulations utilizing the second nearest neighbor modified embedded atom method potentials. The natural spontaneous homogenous nucleation from the Al melt was produced without any influence of pressure, free surface effects and impurities. Initially isothermal crystal nucleation from undercooled melt was studied at different constant temperatures, and later superheated Al melt was quenched with different cooling rates. The crystal structure of nuclei, critical nucleus size, critical temperature for homogenous nucleation, induction time, and nucleation rate were determined. The quenching simulations clearly revealed three temperature regimes: sub-critical nucleation, super-critical nucleation, and solid-state grain growth regimes. The main crystalline phase was identified as face-centered cubic, but a hexagonal close-packed (hcp) and an amorphous solid phase were also detected. The hcp phase was created due to the formation of stacking faults during solidification of Al melt. By slowing down the cooling rate, the volume fraction of hcp and amorphous phases decreased. After the box was completely solid, grain growth was simulated and the grain growth exponent was determined for different annealing temperatures.
Guanglong Huang et al 2024 Modelling Simul. Mater. Sci. Eng. 32 045011
We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.
Orhan Gülcan et al 2024 Modelling Simul. Mater. Sci. Eng. 32 045009
Triply periodic minimal surface (TPMS) lattices have drawn great attention both in academic and industrial perspective due to their outstanding mechanical behaviours. Additive manufacturing (AM) modalities enable the production of these lattices very easily. However, dimensional inaccuracy is still one of the problems that AM still faces with. Manufacturing of these lattices with AM modalities, then measuring the critical dimensions and making design changes accordingly is a costly process. Therefore, it is necessary to predict the dimensional deviation of TPMS lattices before print is a key topic. This study focused on prediction of dimensional deviation of laser powder bed fusion (LPBF) produced gyroid, diamond, primitive, IWP and Fisher-Koch lattices by using thermomechanical simulations. TPMS type, unit cell size, volume fraction, functional grading and part orientation were selected as design variables. Results showed that all the design inputs have effects on dimensional accuracy of LPBF produced parts and TPMS type has the most critical factor. Based on analysis of variance analysis, an optimum lattice configuration was proposed to obtain the lowest dimensional deviation after LPBF build.
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Chen Li et al 2024 Modelling Simul. Mater. Sci. Eng. 32 055014
In the field of femtosecond laser machining, it is essential to select the appropriate process parameters to obtain near thermal damage-free and high efficient machining of SiC wafer. In this work, a method of process parameter optimization for femtosecond laser machining of 4H–SiC was proposed by using the predictive ability of the Artificial Neural Network (ANN) and the optimization algorithm of the non-dominated sorting genetic algorithm (NSGA-II). Firstly, the femtosecond laser was used to fabricate microgrooves on SiC wafers, and the effects of process parameters (laser average power, scanning speed and repetition rate) on groove depth, width, heat affected zone and material removal rate were investigated. Secondly, the ANN model is established based on experimental data. Other experiments verify the accuracy of the model, and the average error in the model's predictions is around 5%. Thirdly, Pareto optimal solutions are obtained by global optimization of the ANN model using the NSGA-II. The experimental results show that the Pareto optimal solutions are effective and reliable. This proposed method offers dependable guidance for the selecting and optimizing process parameters of high hardness and brittle materials in the field of femtosecond laser processing, and reduces the cost of selecting the appropriate processing parameters in the production process. The method can also be extended to other machining means, such as turning and milling.
Rahul Jayakumar et al 2024 Modelling Simul. Mater. Sci. Eng. 32 055013
The metal casting process, which is one of the key drivers of the manufacturing industry, involves several physical phenomena occurring simultaneously like fluid flow, phase change, and heat transfer which affect the casting yield and quality. Casting process modeling involves numerical modeling of these phenomena on a computer. In recent decades, this has become an inevitable tool for foundry engineers to make defect-free castings. To expedite computational time graphics processing units (GPUs) are being increasingly used in the numerical modeling of heat transfer and fluid flow. Initially, in this work a CPU based implicit solver code is developed for solving the 3D unsteady energy equation including phase change numerically using finite volume method which predicts the thermal profile during solidification in the metal casting process in a completely filled mold. To address the computational bottleneck, which is identified as the linear algebraic solver based on the bi-conjugate gradient stabilized method, a GPU-based code is developed using Compute Unified Device Architecture toolkit and was implemented on the GPU. The CPU and GPU based codes are then validated against a commercial casting simulation code FLOW-3D CAST® for a simple casting part and against in-house experimental results for gravity die casting of a simple geometry. Parallel performance is analyzed for grid sizes ranging from 10 × 10 × 10 to 210 × 210 × 210 and for three time-step sizes. The performance of the GPU code based on occupancy and throughput is also investigated. The GPU code exhibits a maximum speedup of 308× compared to the CPU code for a grid size of 210 × 210 × 210 and a time-step size of 2 s.
Damien Tourret et al 2024 Modelling Simul. Mater. Sci. Eng. 32 055012
Bioresorbable Mg-based alloys with low density, low elastic modulus, and excellent biocompatibility are outstanding candidates for temporary orthopedic implants. Coincidentally, metal additive manufacturing (AM) is disrupting the biomedical sector by providing fast access to patient-customized implants. Due to the high cooling rates associated with fusion-based AM techniques, they are often described as rapid solidification processes. However, conclusive observations of rapid solidification in metal AM—attested by drastic microstructural changes induced by solute trapping, kinetic undercooling, or morphological transitions of the solid-liquid interface—are scarce. Here we study the formation of banded microstructures during laser powder-bed fusion (LPBF) of a biomedical-grade Magnesium-rare earth alloy, combining advanced characterization and state-of-the-art thermal and phase-field modeling. Our experiments unambiguously identify microstructures as the result of an oscillatory banding instability known from other rapid solidification processes. Our simulations confirm that LPBF-relevant solidification conditions strongly promote the development of banded microstructures in a Mg–Nd alloy. Simulations also allow us to peer into the sub-micrometer nanosecond-scale details of the solid–liquid interface evolution giving rise to the distinctive banded patterns. Since rapidly solidified Mg alloys may exhibit significantly different mechanical and corrosion response compared to their cast counterparts, the ability to predict the emergence of rapid solidification microstructures (and to correlate them with local solidification conditions) may open new pathways for the design of bioresorbable orthopedic implants, not only fitted geometrically to each patient, but also optimized with locally-tuned mechanical and corrosion properties.
Yanhui Yang et al 2024 Modelling Simul. Mater. Sci. Eng. 32 055011
Through heat treatment experiments and numerical simulations, the effects of the heating temperature (1313–1423 K) and holding time (10–240 min) on the grain growth behavior of the extruded FGH96 alloy were investigated. A two-dimensional cellular automata (CA) model that considered the dissolution of the γ' phase over time and the distribution characteristics with different sizes was developed to explore the grain growth behavior above the γ' phase over-solution temperature (1423 K) and below the γ' sub-solution temperature (1383 K), respectively. The results showed that the rate of grain growth of FGH96 alloy was obviously enhanced when the heating temperature exceeded 1363 K, which was mainly related to the dissolution of the γ' phase, and the grain growth of FGH96 alloy mainly occurred during the initial stage of insulation. The grain growth model of the extruded FHG96 alloy could accurately predict the grain growth behavior, and the simulation results were in good agreement with the experimental results at over-solution temperature or sub-solution temperature. The effects of volume fraction and radius of γ' phase on the grain growth behavior of FGH96 alloy were studied by simulating the grain growth behavior of FGH96 alloy under different sizes and volume fractions of γ' phase. The results follow the Zener relation, and the coefficient n in the Zener relation was determined by fitting the simulation results.
Zbigniew Kozioł 2024 Modelling Simul. Mater. Sci. Eng. 32 055010
Anharmonic inter-atomic potential , n > 1, has been used in molecular dynamics (MD) simulations of stress dynamics of FCC oriented crystal. The model of the chain of masses and springs is found as a convenient and accurate description of simulation results, with masses representing the crystallographic planes. The dynamics of oscillations of two planes is found analytically to be given by Euler's beta functions, and its scaling with non-linearity parameter and amplitude of oscillations, or applied shear pressure is discussed on examples of time dependencies of displacements, velocities, and forces acting on masses (planes). The dynamics of stress penetration from the surface of the sample with multiply-planes (an anharmonic crystal) towards its interior is confirmed to be given exactly as a series of Bessel functions, when n = 2 (Schrödinger and Pater solutions). When n 2 the stress dynamics (wave propagation) in bulk material remains qualitatively of the same nature as in the harmonic case. In particular, results suggest that the quasi-linear relationship between frequency and the wave number is preserved. The speed of the transverse sound component, dependent on sound wave amplitude, is found to be a strongly decreasing function of n. The results are useful in the analysis of any MD simulations under pressure, as they help to understand the dynamics of pressure retarded effects, as well as help design the proper methodology of performing MD simulations in cases such as, for instance, studies of the dynamics of dislocations.
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David Furrer 2023 Modelling Simul. Mater. Sci. Eng. 31 073001
Materials and manufacturing engineering are continuing to advance in part to computational materials and process modeling and associated linkages with associated interdisciplinary efforts across all engineering, manufacturing, and quality disciplines. Computational modeling has enabled virtual processing, prediction and assessment of potential new materials and manufacturing processes, without or with limited need to perform costly and time-consuming physical trials. Development and integration of computational materials and process engineering requires a number of seemingly disparate critical technical elements, making this evolving computational capability very complicated. Accurate and validated models are supporting rapid material, process, and component development, and additionally qualification and certification of new final products through integrated computational materials engineering (ICME). These capabilities are driving further industrial utilization of computational material and process modeling with formalized linkages and integration within multidisciplinary engineering workflows. Past utilization, present applications and potential future development activities indicate that industry has now fully embraced the tools and methods, and overarching engineering framework of ICME.
Vikram Gavini et al 2023 Modelling Simul. Mater. Sci. Eng. 31 063301
Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry, and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.
Gennady Miloshevsky 2022 Modelling Simul. Mater. Sci. Eng. 30 083001
The irradiation of the target surface by an ultrafast femtosecond (fs) laser pulse produces the extreme non-equilibrium states of matter and subsequent phase transformations. Computational modeling and simulation is a very important tool for gaining insight into the physics processes that govern the laser–matter interactions, and, specifically, for quantitative understanding the laser light absorption, electron–ion energy exchange, spallation, melting, warm dense matter regime, vaporization, and expansion of plasma plume. High-fidelity predictive modeling of a variety of these multi-physics processes that take place at various time and length scales is extremely difficult, requiring the coupled multi-physics and multi-scale models. This topical review covers progress and advances in developing the modeling approaches and performing the state-of-the-art simulations of fs laser-pulse interactions with solids and plasmas. A complete kinetic description of a plasma based on the most accurate Vlasov–Maxwell set of equations is first presented and discussed in detail. After that an exact kinetic model that encompasses the microscopic motions of all the individual particles, their charge and current densities, generated electric and magnetic fields, and the effects of these fields on the motion of charged particles in a plasma is briefly reviewed. The methodology of kinetic particle-in-cell (PIC) approach that is well suitable for computational studies of the non-linear processes in laser–plasma interactions is then presented. The hydrodynamic models used for the description of plasmas under the assumption of a local thermodynamic equilibrium include the two-fluid and two-temperature model and its simplifications. The two-temperature model coupled with molecular dynamics (MD) method is finally discussed. Examples are illustrated from research areas such as applications of the fully kinetic, PIC, hydrodynamic, and MD models to studies of ultrafast laser–matter interactions. Challenges and prospects in the development of computational models and their applications to the modeling of ultrafast intense laser–solid and laser–plasma interactions are overviewed.
Chengwei Zang and Pedro E J Rivera-Díaz-del-Castillo 2022 Modelling Simul. Mater. Sci. Eng. 30 063001
High entropy alloys (HEAs) have recently drawn attention due to their excellent mechanical properties across wide temperature ranges. This is attributed to phase stability and a wide variety of strengthening mechanisms in operation. Solid solution, precipitation, dislocation, grain-boundary, twin-boundary and phase-transformation strengthening have been reported to play an important role in controlling their mechanical properties. With a focus on yield strength, this paper reviews the different hardening mechanisms reported in the literature. Mathematical formulations and key constant for describing each mechanism are presented and discussed. A strengthening mechanism modelling strategy for HEA design is outlined.
Marco Salvalaglio and Ken R Elder 2022 Modelling Simul. Mater. Sci. Eng. 30 053001
Comprehensive investigations of crystalline systems often require methods bridging atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are of particular interest as they allow the examination of large systems and time scales while retaining some microscopic details. The so-called phase-field crystal (PFC) model conveniently describes crystals at diffusive time scales through a continuous periodic field which varies on atomic scales and is related to the atomic number density. To go beyond the restrictive atomic length scales of the PFC model, a complex amplitude formulation was first developed by Goldenfeld et al (2005 Phys. Rev. E 72 020601). While focusing on length scales larger than the lattice parameter, this approach can describe crystalline defects, interfaces, and lattice deformations. It has been used to examine many phenomena including liquid/solid fronts, grain boundary energies, and strained films. This topical review focuses on this amplitude expansion of the PFC model and its developments. An overview of the derivation, connection to the continuum limit, representative applications, and extensions is presented. A few practical aspects, such as suitable numerical methods and examples, are illustrated as well. Finally, the capabilities and bounds of the model, current challenges, and future perspectives are addressed.
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Ye et al
An adaptive mesh scheme is introduced for the lattice spring model, where the original triangular cells are subdivided into a set of smaller triangular cells. The scheme is based on geometrical continuity at the heterogeneous mesh boundary, where the refined grid cells intersect the original cell edge. The lattice spring model simulations on the refined grid show a superior computational efficiency to the uniform grid. Each subdivision reduces the original cell edges by a factor of two. The refinement procedure was recursively applied ten times before any marked loss in accuracy was observed. The accuracy of the adaptive model is on par with a regular grid approach. More specifically, the characteristics of fracture cavity are comparable with a uniform grid of the same mesh density as the smallest cells in the adaptive approach. The fracture criterion such as J-integral, the elastic energy of the grid and potential energy change due to fracture growth and strain loading agree well with the theory of a mode I fracture, which enables simulations of process such as sub-critical fracture with a wide dynamic range.
Gupta et al
Shape memory polymers (SMPs) are capable of enduring significant deformations and returning to their original form upon activation by certain external stimuli. However, their restricted mechanical and thermal capabilities have limited their broader application in engineering fields. To address this, the integration of graphene nanoplatelets (GnPs) with SMPs has proven effective in enhancing their mechanical and thermal properties while maintaining inherent shape memory functions. The study evaluated shape memory nanocomposites (SMNCs) using dynamic mechanical, thermogravimetric, and static tensile, flexural, and shape memory tests, along with scanning electron microscopy to analyse tensile fractures. The results indicate that the optimal content of GnP is 0.6 wt%, resulting in excellent shape memory, thermal, and mechanical properties. Specifically, this composition demonstrates a shape recovery ratio of 94.02%, a storage modulus of 4580.07 MPa, a tensile strength of 61.42 MPa, and a flexural strength of 116.37 MPa. Additionally, the incorporation of GnPs into epoxy reduces recovery times by up to 52% at the 0.6 wt% concentration. While there is a slight decrease in the shape fixity ratio from 98.77% to 93.02%, the shape recoverability remains consistently high across all samples. Current finite element (FE) models often necessitate complex, problem-specific user subroutines, which can impede the straightforward application of research findings in real-world settings. To address this, the current study introduces an innovative finite element simulation method using the widely used ABAQUS software to model the thermomechanical behaviour of SMNCs, importantly incorporating the time-dependent viscoelastic behaviour of the material. The effectiveness of this new approach was tested by comparing experimental results from bending test of SMNCs cantilever beam with outcomes derived from FE simulations. The strong agreement between the experimental data and simulation results confirmed the precision and reliability of this novel technique.
Hanson et al
Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the Smoothed Boundary Method (SBM) to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method's capability.
Bauer et al
Science is and always has been based on data, but the terms 'data-centric' and the '4th paradigm of' materials research indicate a radical change in how information is retrieved, handled and research is performed. It signifies a transformative shift towards managing vast data collections, digital repositories, and innovative data analytics methods. The integration of Artificial Intelligence (AI) and its subset Machine Learning (ML), has become pivotal in addressing all these challenges. This Roadmap on Data-Centric Materials Science explores fundamental concepts and methodologies, illustrating diverse applications in electronic-structure theory, soft matter theory, microstructure research and experimental techniques like photoemission, and electron microscopy.
While the roadmap delves into specific areas within the broad interdisciplinary field of materials science, the provided examples elucidate key concepts applicable to a wider range of topics. The discussed instances offer insights into addressing the multifaceted challenges encountered in contemporary materials research.
Iraki et al
The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g., important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images . Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control.
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Bo Ye et al 2024 Modelling Simul. Mater. Sci. Eng.
An adaptive mesh scheme is introduced for the lattice spring model, where the original triangular cells are subdivided into a set of smaller triangular cells. The scheme is based on geometrical continuity at the heterogeneous mesh boundary, where the refined grid cells intersect the original cell edge. The lattice spring model simulations on the refined grid show a superior computational efficiency to the uniform grid. Each subdivision reduces the original cell edges by a factor of two. The refinement procedure was recursively applied ten times before any marked loss in accuracy was observed. The accuracy of the adaptive model is on par with a regular grid approach. More specifically, the characteristics of fracture cavity are comparable with a uniform grid of the same mesh density as the smallest cells in the adaptive approach. The fracture criterion such as J-integral, the elastic energy of the grid and potential energy change due to fracture growth and strain loading agree well with the theory of a mode I fracture, which enables simulations of process such as sub-critical fracture with a wide dynamic range.
Erik Hanson et al 2024 Modelling Simul. Mater. Sci. Eng.
Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the Smoothed Boundary Method (SBM) to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method's capability.
Stefan Bauer et al 2024 Modelling Simul. Mater. Sci. Eng.
Science is and always has been based on data, but the terms 'data-centric' and the '4th paradigm of' materials research indicate a radical change in how information is retrieved, handled and research is performed. It signifies a transformative shift towards managing vast data collections, digital repositories, and innovative data analytics methods. The integration of Artificial Intelligence (AI) and its subset Machine Learning (ML), has become pivotal in addressing all these challenges. This Roadmap on Data-Centric Materials Science explores fundamental concepts and methodologies, illustrating diverse applications in electronic-structure theory, soft matter theory, microstructure research and experimental techniques like photoemission, and electron microscopy.
While the roadmap delves into specific areas within the broad interdisciplinary field of materials science, the provided examples elucidate key concepts applicable to a wider range of topics. The discussed instances offer insights into addressing the multifaceted challenges encountered in contemporary materials research.
Tarek Iraki et al 2024 Modelling Simul. Mater. Sci. Eng.
The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g., important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images . Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control.
Peter Christie et al 2024 Modelling Simul. Mater. Sci. Eng.
Due to attractive mechanical properties, metastable β titanium alloys have become very popular in many industries including aerospace, marine, biomedical, and many more. It is often the complex interplay among the different deformation mechanisms that produces many of the sought-after properties, such as enhanced ductility, super-elasticity, and shape memory effects. Stress induced martensitic transformation is an important deformation mechanism for these alloys. Understanding of it and the influence it has on the microstructural evolution of materials is of great importance. To this end we have developed a crystal plasticity based constitutive model which accounts for both martensitic phase transformation and slip based plasticity simultaneously in metastable β titanium alloys. We present a new formulation for the evolution of martensite transformation, based on physical principles and crystal plasticity theory. To understand and demonstrate this feature of the model, a parametric assessment of the newly developed constitutive model is conducted. This is followed by first of its kind analyses of stress induced martensitic transformation in metastable β titanium alloys. We firstly present validations against uniaxial loading experiments for different metastable β titanium alloys exhibiting stress induced martensite (SIM) transformation. As part of this, single crystal simulations in metastable β titanium alloys are used for the first time to investigate the interaction of individual transformation systems during unconstrained transformation. This study shows good agreement between the experimental and simulated responses during all stages of deformation in which elastic, transformation and finally the slip stage are exhibited. Relatively "strong" and "weak" orientations for transformation are observed, consistent with experimental studies. The work done here demonstrates the ability of this crystal plasticity finite element method (CPFEM) to capture physical mechanisms while bringing new insight about the interaction of different deformation mechanisms in metastable β titanium alloys.
Utkarsh Bhardwaj and Manoj Warrier 2024 Modelling Simul. Mater. Sci. Eng.
The morphology of a collision cascade is an important aspect in understanding 
the formation of defects and their distribution. While the number of 
sub-cascades is an essential parameter to describe the cascade morphology, the 
methods to compute this parameter are limited. We present a method to compute 
the number of sub-cascades from the primary damage state of the collision 
cascade. Existing methods analyze peak damage state or the end of ballistic 
phase to compute the number of sub-cascades which is not always available in 
collision cascade databases. We use density based clustering algorithm from 
unsupervised machine learning domain to identify the sub-cascades from the 
primary damage state. To validate the results of our method we first carry out 
a parameter sensitivity study of the existing algorithms. The study shows that 
the results are sensitive to input parameters and the choice of the time-frame 
analyzed. On a database of 100 collision cascades in W, we show that the method 
we propose, which analyzes primary damage state to predict number of 
sub-cascades, is in good agreement with the existing method that works on the 
peak state. We also show that the number of sub-cascades found with different 
parameters can be used to classify and group together the cascades that have 
similar time-evolution and fragmentation. It is seen that the number of SIA and
vacancies, fraction of defects in clusters and volume of the cascade, decrease with
increase in the number of sub-cascades.
Balduin Katzer et al 2024 Modelling Simul. Mater. Sci. Eng.
Several computational models have been introduced in recent years to
yield comprehensive insights into microstructural evolution analyses. However, the
identification of the correct input parameters to a simulation that corresponds to a
certain experimental result is a major challenge on this length scale. To complement
simulation results with experimental data (and vice versa) is not trivial since, e.g.,
simulation model parameters might lack a physical understanding or uncertainties
in the experimental data are neglected. Computational costs are another challenge
mesoscale models always have to face, so comprehensive parameter studies can be
costly. In this paper, we introduce a surrogate model to circumvent continuum
dislocation dynamics simulation by a data-driven linkage between well-defined input
parameters and output data and vice versa. We present meaningful results for a
forward surrogate formulation that predicts simulation output based on the input
parameter space, as well as for the inverse approach that derives the input parameter
space based on simulation as well as experimental output quantities. This enables, e.g.,
a direct derivation of the input parameter space of a continuum dislocation dynamics
simulation based on experimentally provided stress-strain data.
Zbigniew Kozioł 2024 Modelling Simul. Mater. Sci. Eng. 32 055010
Anharmonic inter-atomic potential , n > 1, has been used in molecular dynamics (MD) simulations of stress dynamics of FCC oriented crystal. The model of the chain of masses and springs is found as a convenient and accurate description of simulation results, with masses representing the crystallographic planes. The dynamics of oscillations of two planes is found analytically to be given by Euler's beta functions, and its scaling with non-linearity parameter and amplitude of oscillations, or applied shear pressure is discussed on examples of time dependencies of displacements, velocities, and forces acting on masses (planes). The dynamics of stress penetration from the surface of the sample with multiply-planes (an anharmonic crystal) towards its interior is confirmed to be given exactly as a series of Bessel functions, when n = 2 (Schrödinger and Pater solutions). When n 2 the stress dynamics (wave propagation) in bulk material remains qualitatively of the same nature as in the harmonic case. In particular, results suggest that the quasi-linear relationship between frequency and the wave number is preserved. The speed of the transverse sound component, dependent on sound wave amplitude, is found to be a strongly decreasing function of n. The results are useful in the analysis of any MD simulations under pressure, as they help to understand the dynamics of pressure retarded effects, as well as help design the proper methodology of performing MD simulations in cases such as, for instance, studies of the dynamics of dislocations.
Yixiu Luo et al 2024 Modelling Simul. Mater. Sci. Eng. 32 055009
Understanding the phononic origin of the infrared (IR) dielectric properties of yttria (Y2O3) and other rare-earth sesquioxides (RE2O3) is a fundamental task in the search of appropriate RE2O3 materials that serve particular IR optical applications. We herein investigate the IR dielectric properties of RE2O3 (RE = Y, Gd, Ho, Lu) using density functional theory-based phonon calculations and Lorentz oscillator model. The abundant IR-active optical phonon modes that are available for effective absorption of photons result in high reflectance of RE2O3, among which four IR-active modes originated from large distortions of REO6 octahedra are found to contribute dominantly to the phonon dielectric constants. Particularly, the present calculation method by considering one-phonon absorption process is demonstrated with good reliability in predicting the IR dielectric parameters of RE2O3 at the far-IR as well as the vicinity of mid-IR region, and the potential cutoff frequency/wavelength of its applicability is disclosed as characterized by the maximum frequency of IR-active longitudinal phonon modes. The results deepen the understanding on IR dielectric properties of RE2O3, and aid the computational design of materials with appropriate IR properties.
Xiaohua Hu et al 2024 Modelling Simul. Mater. Sci. Eng.
An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al-12Ce alloy and a ternary Al-12Ce-0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based crystal plasticity models to predict materials performance. From this study, it is shown that the elastic constants of Al11Ce3 intermetallics calculated from DFT calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al11Ce3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress (CRSS) of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al-Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al-Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.