Modelling and Simulation in Materials Science and Engineering

An interatomic potential, traditionally regarded as a mathematical function, serves to depict atomic interactions within molecules or solids by expressing potential energy concerning atom positions. These potentials are pivotal in materials science and engineering, facilitating atomic-scale simulations, predictive material behavior, accelerated discovery, and property optimization. Notably, the landscape is evolving with machine learning transcending conventional mathematical models. Various machine learning-based interatomic potentials, such as artificial neural networks, kernel-based methods, deep learning, and physics-informed models, have emerged, each wielding unique strengths and limitations. These methods decode the intricate connection between atomic configurations and potential energies, offering advantages like precision, adaptability, insights, and seamless integration. The transformative potential of machine learning-based interatomic potentials looms large in materials science and engineering. They promise tailor-made materials discovery and optimized properties for specific applications. Yet, formidable challenges persist, encompassing data quality, computational demands, transferability, interpretability, and robustness. Tackling these hurdles is imperative for nurturing accurate, efficient, and dependable machine learning-based interatomic potentials primed for widespread adoption in materials science and engineering. This roadmap offers an appraisal of the current machine learning-based interatomic potential landscape, delineates the associated challenges, and envisages how progress in this domain can empower atomic-scale modeling of the composition-processing-microstructure-property relationship, underscoring its significance in materials science and engineering.

Machine learning interatomic potentials (MLIPs) have massively changed the field of atomistic modeling. They enable the accuracy of density functional theory in large-scale simulations while being nearly as fast as classical interatomic potentials (IPs). Over the last few years, a wide range of different types of MLIPs have been developed, but it is often difficult to judge which approach is the best for a given problem setting. For the case of structurally and chemically complex solids, namely Al–Cu–Zr and Si–O, we benchmark a range of MLIP approaches, in particular, the Gaussian approximation potential, high-dimensional neural network potentials, moment tensor potentials, the atomic cluster expansion (ACE) in its linear and nonlinear version, neural equivariant interatomic potentials (NequIP), Allegro, and MACE. We find that nonlinear ACE and the equivariant, message-passing graph neural networks NequIP and MACE form the Pareto front in the accuracy vs. computational cost trade-off. In case of the Al–Cu–Zr system we find that MACE and Allegro offer the highest accuracy, while NequIP outperforms them for Si–O. Furthermore, GPUs can massively accelerate the MLIPs, bringing them on par with and even ahead of non-accelerated classical IPs with regards to accessible timescales. Finally, we explore the extrapolation behavior of the corresponding potentials, probe the smoothness of the potential energy surfaces, and estimate the user friendliness of the corresponding fitting codes and molecular dynamics interfaces.

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 and its subset machine learning, 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, atom probe tomography, 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.

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.

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.

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/.

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.

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.

Models based on the coupling of phase-field methods with fluid dynamics are commonly used to simulate flow in complex geometries or in conjunction with phase transformation. Thereby, diffuse interfaces between fluid and solid are used, which requires the corresponding diffusive application of the boundary conditions with regard to the flow. While different approaches to achieving this are found in literature, a quantitative comparison of these methods is still missing. The present work aims to establish benchmarks addressing the diffuse fluid–solid transition for interfaces with and without wall velocity. Furthermore, different models from literature are revisited and comparatively discussed in detail. Using the defined benchmark cases, a quantitative assessment of these models is performed to investigate their accuracy for varying interface widths and different phase-field profiles. The results show that the best choice of the diffuse model is problem-dependent.

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.

Choosing a suitable potential model to study dynamic processes in novel structures is an ambitious task often relying on chemical intuition. This paper addresses this challenge through a case study of diaphites, diamond-graphite nanocomposites, that are the only naturally occurring crystalline form of carbon featuring both sp³ and sp² hybridized atoms. Since their synthesis is expensive and difficult to control, molecular dynamics (MD) simulations of their formation would be highly valuable. However, none of the available carbon potentials explicitly includes diaphites in their parameterization. Here, we benchmark several well-established carbon potentials (Tersoff 1989, Tersoff 1994, REBO-II, LCBOP-I, AIREBO, AIREBO-M, GAP-20, ACE) against ab initio MD (AIMD) at the PBE+D2 level of theory. Comparison of structural labeling disqualified Tersoff 1989, Tersoff 1994, REBO-II, AIREBO, and AIREBO-M. To enable long-timescale simulations on systems of a few thousand atoms, an machine-learning (ML)-AIMD model was developed using AIMD acceleration with an on-the-fly Gaussian approximation potential (GAP). ML-AIMD accurately reproduced AIMD results and was therefore used as a benchmark. Extended testing revealed that ACE is the most transferable and computationally efficient potential for MD simulations of diaphites, reproducing the sp² fraction across all temperatures at a cost at least four times lower than GAP-20. LCBOP-I performed comparably below 2000 K and remains preferable when computational resources are limited. The presented benchmarking framework efficiently identifies the most suitable potentials and provides a general strategy for selecting MD models for novel materials.

The effect of grain boundary (GB) additions of Al, Ta, Ni, Zr, and Ag on the plastic deformation and mechanical properties of nanocrystalline copper is investigated using molecular dynamics simulations. The simulation results indicate that adding Al, Ta, Zr, Ag, and Ni to the GBs can increase the flow stress of nanocrystalline copper by 79.0%, 15.5%, 6.7%, 4.9%, and 4.5%, respectively. Moreover, the flow stress increases with increasing concentrations of Al and Ta, while for Zr and Ag the flow stress increases first and then decreases with increasing their concentrations. The strengthening effect is related to the grain size refinement induced by the GB doping and plastic deformation. At 10% strain, the average grain size of the Cu-8 at.% Al sample is reduced by 15.8% relative to the unstrained pure nanocrystalline copper, representing the largest grain refinement among those doping elements. The grain size refinement cannot be entirely attributed to the atomic size mismatch between the addition and the matrix atoms. The GBs are significantly broadened by the additions of Al, Ta, and Zr. The additions of Al, Ta, Zr, and Ag decrease the dislocation density induced by both the initial thermal relaxation and plastic deformation, which suggests that these GB additions inhibit the dislocation-based deformation mechanism. The additions of Al and Ta still have significant strengthening effect on nanocrystalline copper at high temperature, which increase the flow stress by 49.2% and 12.2% at a concentration of 8 at.%, respectively. These findings indicate that both the types of addition elements and their concentrations are critical factors to be taken into account when utilizing the GB doping approach to strengthen nanocrystalline copper.

This work presents the computational design of a lightweight jet engine mount bracket based on multiscale experimental characterization of recycled AA2024 aluminum alloy. The alloy was processed through melting and casting, followed by solution heat treatment at 530 °C for 1 h and subsequent water quenching. Three heat treatment conditions were investigated: the solutionized condition without aging, and two T6-aged conditions with artificial aging at 180 °C for 2 and 24 h, respectively. Microstructural evolution was analyzed using scanning electron microscopy and energy-dispersive spectroscopy, supported by CALPHAD thermodynamic simulations. Mechanical behavior was evaluated via Vickers microhardness and compression testing. The T6 condition aged for 24 h at 180 °C exhibited the highest mechanical performance, with a 60% increase in strength compared to the solutionized condition. These results were used as input for finite element simulation and design optimization of a GE90-94B jet engine bracket under four critical loading conditions. The optimization achieved a 39% mass reduction while maintaining the minimum safety factor of 1.5. This integration of multiscale experiments and virtual design optimization demonstrates the viability of recycled AA2024 aluminum for producing lightweight aeronautical components.

Silicon nitride (Si₃N₄) ceramics are regarded as significant high-temperature structural materials owing to their superior mechanical and thermal characteristics. However, the performance of these materials is often governed by their grain boundary structure. In this study, we employed molecular dynamics simulations to investigate the effect of grain boundary interface matching on the thermal and mechanical properties of β-Si₃N₄. Various grain boundary configurations were constructed using the grain boundary inter-connection (GBIC) model and characterized by their planar coincident site density (PCSD). Our results reveal that grain boundaries with higher PCSD values, indicating better atomic registry, exhibit significantly higher thermal conductivity. The discrepancy in thermal conductivity between the grain boundary and the ideal crystal diminishes as the PCSD increases. Mechanically, high-PCSD grain boundaries demonstrate a steeper stress-strain response during tension, correlating with enhanced elastic modulus and ultimate tensile strength. This work elucidates that optimizing grain boundary structures through interface matching is a viable strategy for synergistically improving the thermal and mechanical performance of Si₃N₄ ceramics, providing a theoretical foundation for fabricating advanced ceramics with superior properties.

Observation of glass properties including the glass transition temperature T_g is one of the most challenging problems for atomistic simulations due to the complexity of composition and slow time evolution rates. To address the issue, robust machine learning potentials trained with accurate ab initio data can be employed. In this paper, a prospective glass for immobilization of nuclear waste with 0.25 Na₂O–0.25 Al₂O₃–0.5 P₂O₅ (mass fraction) composition was studied via a neural network potential. We used 42 independent ab initio calculations as a dataset. The glass was obtained by slow cooling during 96 ns from the molten state down to room temperature. We used an extrapolation technique to assess the true glass transition temperature for infinitely slow cooling and found that the resulting T_g of 715 K agrees well with the experimentally observed value 682 K. The specific heat was studied for a temperature range up to T = 1500 K. Also, thermal conductivity was calculated using the non-equilibrium molecular dynamics. Among other properties, Young’s modulus, thermal diffusivity, and vibrational density of states were calculated. The reliability of the developed model was further confirmed by comparison with the experimentally measured density and Raman spectrum.

Level-set methods provide a powerful computational framework for simulating free boundary problems in materials science. This paper presents a unified perspective on their application to two distinct phenomena: multicomponent alloy solidification and epitaxial island growth. Although these problems differ significantly in physical mechanisms and characteristic length scales, they can both be effectively addressed within the level-set framework, highlighting the versatility of the method across diverse applications. We outline the mathematical formulations and highlight computational advances and common features across applications. This overview highlights the role of level-set methods as a foundational tool in predictive materials modeling.

The level-set (LS) method has been widely spread since its introduction in 1988. One of its main features is that interfaces are represented through signed distance functions, and the distance property eases the smoothing of discontinuities across an interface, and the computation of normal vectors and mean curvatures. This property can be lost whenever the LS function is evolved, for instance, through an LS transport equation. Numerous studies proposing so-called LS reinitialization methods to restore the distance property have been published since 1988. This paper is a review of numerical developments on LS reinitialization in the past decade (2014–2024). LS reinitialization methods are classified into three categories: direct methods which geometrically compute distances, local indirect methods which solve the Eikonal equation point-by-point, and global indirect methods which solve the Eikonal equation for all points at once. The review focuses on numerical methods and investigates the following questions. Can it be implemented in a parallel computing environment with nearly optimal scalability? Can it be used with any approximation method, and is it compatible with unstructured grids? Can it be extended to reach higher-order convergence rates? Can it be combined with mass change error attenuation techniques? Does it involve any numerical parameters that may affect its robustness? Is it limited only to some applications? Through a quantitative and qualitative analysis of the past decade’s literature, this review paper proposes novel insights on LS reinitialization. Research on direct methods should focus on parallel efficiency and robust higher-order distance computation techniques. More attention should be given to local indirect methods, especially regarding parallel and higher-order algorithms for unstructured grids. Control parameters for global indirect methods should be better determined or eliminated. More research is needed on the issue of blind spots in two-phase problems involving moving contact lines and their elimination.

An interatomic potential, traditionally regarded as a mathematical function, serves to depict atomic interactions within molecules or solids by expressing potential energy concerning atom positions. These potentials are pivotal in materials science and engineering, facilitating atomic-scale simulations, predictive material behavior, accelerated discovery, and property optimization. Notably, the landscape is evolving with machine learning transcending conventional mathematical models. Various machine learning-based interatomic potentials, such as artificial neural networks, kernel-based methods, deep learning, and physics-informed models, have emerged, each wielding unique strengths and limitations. These methods decode the intricate connection between atomic configurations and potential energies, offering advantages like precision, adaptability, insights, and seamless integration. The transformative potential of machine learning-based interatomic potentials looms large in materials science and engineering. They promise tailor-made materials discovery and optimized properties for specific applications. Yet, formidable challenges persist, encompassing data quality, computational demands, transferability, interpretability, and robustness. Tackling these hurdles is imperative for nurturing accurate, efficient, and dependable machine learning-based interatomic potentials primed for widespread adoption in materials science and engineering. This roadmap offers an appraisal of the current machine learning-based interatomic potential landscape, delineates the associated challenges, and envisages how progress in this domain can empower atomic-scale modeling of the composition-processing-microstructure-property relationship, underscoring its significance in materials science and engineering.

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 and its subset machine learning, 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, atom probe tomography, 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.

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.

Mechanical properties are critical to material performance and are influenced by external conditions, notably temperature. Uncovering the mechanisms through which temperature influences these properties is essential for material development and application. In our previous work, an atomic-scale-structure-based model was introduced to predict the Young's modulus of various doped amorphous carbons, expressed as E= k Keff (CNeff-2.0)1.5. This model emphasizes two critical material properties: effective coordination number (CNeff) and effective bond stiffness (Keff). However, this model is restricted to the predictions at room temperature, its applicability must be extended to broader temperature ranges to address the challenges posed by complex thermal environments. Research indicates that the temperature may influence the Young's modulus by both CNeff and Keff. These temperature effects could be incorporated by changing the constant pre-factor k to a temperature-dependent function k(T). Through high-throughput molecular dynamics (MD) simulation statistics, we obtained the detailed expression of k(T), ultimately achieving a successful extension of the previous model. While, compared to the previous work, the new model keeps errors within 50.0 GPa for Young’s modulus predictions across 100~1000 K, with a fitted R² of 0.987, demonstrating a high predictive accuracy. In summary, this foundational work further explores the relationships among external conditions, atomic-scale structure, and Young's modulus. It is expected that this work will greatly benefit the development, preparation, and utilization of novel materials.

Steam turbines play a crucial role in power generation, requiring high efficiency, reliability, and extended service life. The rotor shaft, a critical structural component, develops residual stresses during manufacturing stages such as heat treatment, which are intended to enhance mechanical properties but can adversely affect dimensional stability and fatigue life. The specimen analyzed is a coupon extracted from a forged rotor shaft with identical alloy composition, reduction ratio, and heat-treatment history. Geometry and size effects may influence the stress distribution, but this approach preserves industrial relevance. A finite element based thermomechanical framework was developed to predict quenching-induced residual stresses and validated through X-ray diffraction (XRD) measurements. The model demonstrated strong predictive capability, with a mean relative error of 9.29%, indicating its reliability for engineering design and residual stress evaluation. The model predicts the interior three-dimensional residual stress field under the following assumptions: no phase-transformation strains or transformation plasticity, temperature-independent multilinear isotropic hardening, and stage-wise constant heat-transfer coefficient and emissivity. Precise representation of stress distributions allows refinement of heat treatment protocols, enhancement of structural integrity, and reduction of reliance on costly trial-and-error experiments. Although this investigation focused on experimentally validated FEA (Finite Element Analysis) of the test coupon, the methodology provides a foundation for potential integration into future Integrated Computational Materials Engineering (ICME) frameworks, where such predictive models could be combined with multiscale materials design and process optimization to support industrial component development.

Tungsten ($W$) is widely valued for its exceptional thermal stability, mechanical strength, and corrosion resistance, making it an ideal candidate for high-performance military and aerospace applications. However, its high melting point and limited room-temperature plasticity pose significant challenges for processing $W$ using additive manufacturing (AM). Cold spray (CS), a solid-state AM process that relies on high-velocity particle impact and plastic deformation, offers a promising route for additive manufacturing of $W$, yet conventional CS fails to induce sufficient plastic deformation for effective bonding. In this study, we employ atomistic simulations to investigate the effect of ultrasonic perturbation in enhancing plastic deformation during CS of $W$, with a focus on acoustoplasticity-driven deformation mechanism. We show that ultrasonic perturbation leads to pronounced acoustic softening and promotes transient temperature elevation at the particle-substrate and particle-particle interfaces, thereby enhancing plastic deformation compared to non-ultrasound-assisted CS. Additionally, our results show that the coupled effects of acoustic softening and enhanced transient thermal activation lead to substantial improvements in interfacial bonding across a wide range of impact velocities, particle sizes, and ultrasonic parameters. Finally, we analyze the feasibility of ultrasound-assisted CS for manufacturing heterogeneous interfaces consisting of an equimolar Vanadium ($V$)-Tungsten ($W$) coating on a $W$ substrate. Simulations reveal distinct mechanical behavior and dislocation densities compared to the homogeneous $W$ on $W$ CS configurations. Overall, this work highlights the potential of ultrasound-assisted cold spray as an effective strategy for manufacturing uniform coatings and engineered alloys, thereby addressing critical limitations in the additive manufacturing of refractory metals.

The present study systematically investigated the cavitation behavior and nanoparticle dispersion in molten aluminum (Al) under low-frequency oscillating electromagnetic forces. A coupled multiphysics numerical model was established, integrating computational fluid dynamics (CFD), the revised Schnerr-Sauer cavitation model, and the discrete phase model (DPM). The revised cavitation model was validated through comparison with analytical solutions of the Epstein-Plesset equation, thereby confirming its reliability for simulating cavitation in molten Al. The model was subsequently applied to analyze the effects of oscillating electromagnetic force parameters (type, amplitude: 3.09–5.57×10⁶ N·m⁻³, and frequency: 50–300 Hz) on cavitation distribution and nanoparticle dispersion of 1.0 wt.% SiC (30–80 nm). Results demonstrated that the effectiveness of nanoparticle dispersion in the melt depended strongly on cavitation intensity, as both insufficient and excessive vapor volume fractions(VVF) reduced dispersion uniformity. Optimal dispersion occurred at a frequency of 50 Hz and an amplitude of 4.33×10⁶ N·m⁻³, corresponding to a cavitation VVF of approximately 2%, at which cavitation-induced flow reached a maximum without compromising flow stability. Relative to unidirectional excitation, bidirectional oscillating electromagnetic forces produced a more symmetric melt flow field, which facilitated more uniform cavitation and nanoparticle distribution. Increasing the force amplitude enlarged cavitation regions and intensified melt mixing, which improved dispersion, whereas excessively high amplitudes caused cavitation saturation and destabilized the flow. For unidirectional forcing, higher frequencies progressively weakened cavitation by shortening the negative-pressure duration and enhancing the skin effect. By contrast, under bidirectional forcing, increasing frequency initially promoted cavitation through pressure-wave superposition, but subsequently decreased dispersion efficiency owing to insufficient negative-pressure duration and a more pronounced skin effect. The present study may therefore serve as a theoretical basis for the controlled fabrication of nanoparticle-reinforced Al matrix composites via low-frequency electromagnetic processing.

Precise prediction of fatigue life is vital to ensure structural integrity in aerospace components like fuselage frames, bulkheads, and wing fittings. These parts are generally manufactured from AA2014 due to its high strength, fatigue resistance, and superior strength-to-weight ratio. The present work proposes a machine learning (ML)-driven approach for fatigue life prognosis in AA2014 to overcome the limitations of traditional fatigue life prediction models. Experimental fatigue tests were conducted at different maximum stress levels (320-350 MPa) and loading frequencies (9 Hz and 12 Hz) to generate a comprehensive dataset. This dataset was used to develop the ML models and performance metrics like R2, RMSE, and MAPE were recorded for comparative analysis of the three MLmodels: Random Forest Regression (RFR), Support Vector Regression (SVR), and Gaussian Process Regression (GPR). GPR was found to be the most reliable model for fatigue prognosis in AA2014 as it yielded the highest predictive accuracy with an R2 of 0.9874, RMSE of 618.2, and a MAPE of 1.89%. The work proves that ML can greatly enhance fatigue life predictive accuracy and drastically reduce the dependence on experimental runs. Future studies can investigate hybrid AI models by integrating deep learning and physics-informed ML approaches to enhance prediction reliability and expand applicability to other aerospace-grade alloys.

Choosing a suitable potential model to study dynamic processes in novel structures is an ambitious task often relying on chemical intuition. This paper addresses this challenge through a case study of diaphites, diamond-graphite nanocomposites, that are the only naturally occurring crystalline form of carbon featuring both sp³ and sp² hybridized atoms. Since their synthesis is expensive and difficult to control, molecular dynamics (MD) simulations of their formation would be highly valuable. However, none of the available carbon potentials explicitly includes diaphites in their parameterization. Here, we benchmark several well-established carbon potentials (Tersoff 1989, Tersoff 1994, REBO-II, LCBOP-I, AIREBO, AIREBO-M, GAP-20, ACE) against ab initio MD (AIMD) at the PBE+D2 level of theory. Comparison of structural labeling disqualified Tersoff 1989, Tersoff 1994, REBO-II, AIREBO, and AIREBO-M. To enable long-timescale simulations on systems of a few thousand atoms, an machine-learning (ML)-AIMD model was developed using AIMD acceleration with an on-the-fly Gaussian approximation potential (GAP). ML-AIMD accurately reproduced AIMD results and was therefore used as a benchmark. Extended testing revealed that ACE is the most transferable and computationally efficient potential for MD simulations of diaphites, reproducing the sp² fraction across all temperatures at a cost at least four times lower than GAP-20. LCBOP-I performed comparably below 2000 K and remains preferable when computational resources are limited. The presented benchmarking framework efficiently identifies the most suitable potentials and provides a general strategy for selecting MD models for novel materials.

Tungsten ($W$) is widely valued for its exceptional thermal stability, mechanical strength, and corrosion resistance, making it an ideal candidate for high-performance military and aerospace applications. However, its high melting point and limited room-temperature plasticity pose significant challenges for processing $W$ using additive manufacturing (AM). Cold spray (CS), a solid-state AM process that relies on high-velocity particle impact and plastic deformation, offers a promising route for additive manufacturing of $W$, yet conventional CS fails to induce sufficient plastic deformation for effective bonding. In this study, we employ atomistic simulations to investigate the effect of ultrasonic perturbation in enhancing plastic deformation during CS of $W$, with a focus on acoustoplasticity-driven deformation mechanism. We show that ultrasonic perturbation leads to pronounced acoustic softening and promotes transient temperature elevation at the particle-substrate and particle-particle interfaces, thereby enhancing plastic deformation compared to non-ultrasound-assisted CS. Additionally, our results show that the coupled effects of acoustic softening and enhanced transient thermal activation lead to substantial improvements in interfacial bonding across a wide range of impact velocities, particle sizes, and ultrasonic parameters. Finally, we analyze the feasibility of ultrasound-assisted CS for manufacturing heterogeneous interfaces consisting of an equimolar Vanadium ($V$)-Tungsten ($W$) coating on a $W$ substrate. Simulations reveal distinct mechanical behavior and dislocation densities compared to the homogeneous $W$ on $W$ CS configurations. Overall, this work highlights the potential of ultrasound-assisted cold spray as an effective strategy for manufacturing uniform coatings and engineered alloys, thereby addressing critical limitations in the additive manufacturing of refractory metals.

Level-set methods provide a powerful computational framework for simulating free boundary problems in materials science. This paper presents a unified perspective on their application to two distinct phenomena: multicomponent alloy solidification and epitaxial island growth. Although these problems differ significantly in physical mechanisms and characteristic length scales, they can both be effectively addressed within the level-set framework, highlighting the versatility of the method across diverse applications. We outline the mathematical formulations and highlight computational advances and common features across applications. This overview highlights the role of level-set methods as a foundational tool in predictive materials modeling.

Models based on the coupling of phase-field methods with fluid dynamics are commonly used to simulate flow in complex geometries or in conjunction with phase transformation. Thereby, diffuse interfaces between fluid and solid are used, which requires the corresponding diffusive application of the boundary conditions with regard to the flow. While different approaches to achieving this are found in literature, a quantitative comparison of these methods is still missing. The present work aims to establish benchmarks addressing the diffuse fluid–solid transition for interfaces with and without wall velocity. Furthermore, different models from literature are revisited and comparatively discussed in detail. Using the defined benchmark cases, a quantitative assessment of these models is performed to investigate their accuracy for varying interface widths and different phase-field profiles. The results show that the best choice of the diffuse model is problem-dependent.

The present study compares four modelling approaches to predict the mechanical behaviour of additively manufactured honeycomb structures. Cellular structures are increasingly employed in energy absorption applications due to their tunable deformation characteristics and lightweight architecture. Accurate modelling of such structures remains challenging, particularly when accounting for the anisotropic and nonlinear behaviour induced by fused-filament fabrication. While detailed modelling approaches based on raster orientation can improve accuracy, they are often computationally expensive and impractical for complex geometries. To address this, isotropic and bimodular assumptions are commonly adopted to simplify the analysis. In this study, the mechanical behaviour of re-entrant honeycomb (RH) structures fabricated using poly(lactic) acid was investigated through a combination of experiments and finite element simulations. Four modelling approaches: (i) elastoplastic (EP), (ii) elastic-perfectly plastic (EPP), (iii) bimodular EP (B-EP), and (iv) bimodular EPP (B-EPP) were evaluated in Abaqus/Standard. Additionally, experimental compression tests were conducted to benchmark numerical predictions of stiffness, peak force, plateau stress, energy absorption, and deformation patterns. All modelling approaches successfully captured the characteristic deformation modes observed experimentally, indicating that the global structural behaviour is primarily governed by geometry. However, significant differences were observed in the quantitative response. The EP model provided the closest agreement with experimental measurements for plateau stress and energy absorption, while the B-EPP model offered improved prediction of the initial stiffness and plateau phase at larger displacements despite underestimating peak force. These findings highlight that, although qualitative deformation patterns are reproduced by all models, an appropriate constitutive formulation is crucial for accurately predicting the mechanical performance of 3D-printed cellular structures.

Continuum-scale material deformation models, such as crystal plasticity (CP), can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e. mesoscale) models. The procedure to generate and extract the relevant information is however typically complex and ad hoc, involving decision and intervention by domain experts, leading to long development times. In this study, we develop a principled approach for calibration of continuum-scale models using lower scale information by representing a CP flow rule as a Gaussian process model. This representation allows for efficient parameter space exploration, guided by the uncertainty embedded in the model through a process known as Bayesian optimization (BO). We demonstrate a semi-autonomous BO loop which instantiates discrete dislocation dynamics simulations whose initial conditions are automatically chosen to optimize the uncertainty of a model CP flow rule. Our self-guided computational pipeline efficiently generated a dataset and corresponding model whose error, uncertainty, and physical feature sensitivities were validated with comparison to an independent dataset four times larger, demonstrating a valuable and efficient active learning implementation readily transferable to similar material systems.

Tungsten–Chromium (W–Cr) alloys are promising candidates for extreme environments due to their excellent high-temperature mechanical properties as well as superior corrosion and irradiation resistance. However, their large positive enthalpy of mixing causes a miscibility gap, driving phase separation that significantly affects material performance and processing. In this work, we developed a three-dimensional Cahn–Hilliard phase field model to simulate the phase separation kinetics of the W–Cr system, incorporating chemical free energy, gradient energy, and coupling concentration evolution with heat diffusion to account for thermal effects. A key contribution of this study is the explicit introduction of temperature-scaled Gaussian noise directly into the concentration field, thereby avoiding the need to embed noise into subsequent partial differential equations. This approach provides a more realistic representation of local fluctuations arising from concentration fluctuations and thermal heterogeneities. Using this model, we explore the microstructure evolution under compositional and temperature gradients, focusing on hierarchical structures relevant to nanolayered systems, diffusion couples, and functionally graded materials. Our results demonstrate that composition and temperature gradients play a critical role in governing mesoscale dynamics, where spinodal decomposition and nucleation can occur simultaneously. These findings provide valuable insight into the fundamental mechanisms governing phase stability, coarsening, and degradation in W–Cr alloys, informing the design and processing of advanced materials for nuclear fusion applications and high-temperature protective coatings. Moreover, the model is general and can be readily extended to other material systems.

Accurately predicting the nonlinear viscoelastic behaviour of materials such as polymers remains a key challenge, particularly when only limited experimental data are available. While recurrent neural networks (RNNs) are often used to capture path-dependent material responses, they suffer from training instabilities and poor extrapolation capabilities. This study addresses this gap by developing an alternative approach with a hybrid, thermodynamically-based framework that combines a linear generalised Maxwell model with a multilayer perceptron (MLP). The Maxwell model acts as a ‘physics-based’ encoding layer, providing interpretable internal variables that represent the material’s deformation history. Unlike RNNs, MLPs are better suited for capturing complex nonlinear relationships without relying on memory cells, thereby improving generalisation beyond the training domain. The parameters of the mechanical model and the neural network are jointly optimised. A residual connection allows the network to correct the Maxwell model’s output. The proposed model, referred to as Mech-TANN, accurately reproduces nonlinear viscoelastic behaviour using only forty noisy data points from synthetic shear tests. It achieves less than 7% prediction error on test data with a noise level of 2% of the maximum signal amplitude. With four times the data, the precision improves tenfold. It demonstrates excellent extrapolation to larger strain amplitudes and unseen loading types, including relaxation tests. The combination of mechanical encoding and thermodynamic constraints yields a data-efficient and generalisable modelling framework that benefits from physically motivated inductive bias for complex time-dependent materials.

pyPFC is a comprehensive open-source Python package for setting up, running and analyzing 3D phase field crystal (PFC) simulations. The object-oriented code is designed to take full advantage of GPU acceleration, but can also be ran on purely CPU-based systems. The overarching ambition with the pyPFC package is to provide an easily accessible and computationally efficient PFC simulation framework, suitable for algorithm and method development and for those interested in making their first experiments with PFC, while also being versatile and powerful enough for more demanding scientific investigations. Details of the underlying PFC formulation are given and simulation examples are provided to illustrate a range of pyPFC functionalities.

Highly regular porous armchair graphene nanoribbons having a width of 12 atoms were synthesized recently. A model for investigating the quantum transport properties in such nanoribbons is developed by using a tight-binding lattice. The mode propagation in the nanoribbons is examined by analyzing the equations of motion. The lattice-Green-function technique is employed in calculating the quantum transmission coefficients of the Bloch modes. The calculation method of the lattice Green functions is adjusted to be suitable for the porous geometry of the nanoribbons for the situations where the conventional method is inapplicable due to the presence of the pores. The quantum transport exhibits a Fabry–Pérot interference when the porous nanoribbon is sandwiched by pristine nanoribbons. The lower envelop of the interference oscillation agrees with the prediction derived from the scattering properties at a single porous-pristine junction in the single-mode transport regime. While the oscillation envelop cannot be predicted in general in the multi-mode transport regime due to the random superposition of the oscillation components associated with the individual modes, the transmission is found to become even less than the predicted lower bound occasionally. In addition, the modes are not always independent from each other in the superposition. The comparison of the envelop form is made also for the quantum interference properties in a porous-pristine-porous junction. The violation of the lower bound is extensive including the single-mode regime when the coexisting Fano resonance states appear to fuse with the Fabry–Pérot interference states.

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/.

We present a computational method for identifying partial and interfacial dislocations in atomistic models of crystals with defects. Our automated algorithm is based on a discrete Burgers circuit integral over the elastic displacement field and is not limited to specific lattices or dislocation types. Dislocations in grain boundaries and other interfaces are identified by mapping atomic bonds from the dislocated interface to an ideal template configuration of the coherent interface to reveal incompatible displacements induced by dislocations and to determine their Burgers vectors. In addition, the algorithm generates a continuous line representation of each dislocation segment in the crystal and also identifies dislocation junctions.

Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as common neighbour analysis, rely on interatomic distances (or thresholds thereof) to classify atomic structure. As a consequence they are sensitive to strain and thermal displacements, and preprocessing such as quenching or temporal averaging of the atomic positions is necessary to provide reliable identifications. We propose a new method, polyhedral template matching (PTM), which classifies structures according to the topology of the local atomic environment, without any ambiguity in the classification, and with greater reliability than e.g. common neighbour analysis in the presence of thermal fluctuations. We demonstrate that the method can reliably be used to identify structures even in simulations near the melting point, and that it can identify the most common ordered alloy structures as well. In addition, the method makes it easy to identify the local lattice orientation in polycrystalline samples, and to calculate the local strain tensor. An implementation is made available under a Free and Open Source Software license.

We describe a novel method for extracting dislocation lines from atomistic simulation data in a fully automated way. The dislocation extraction algorithm (DXA) generates a geometric description of dislocation lines contained in an arbitrary crystalline model structure. Burgers vectors are determined reliably, and the extracted dislocation network fulfills the Burgers vector conservation rule at each node. All remaining crystal defects (grain boundaries, surfaces, etc), which cannot be represented by one-dimensional dislocation lines, are output as triangulated surfaces. This geometric representation is ideal for visualization of complex defect structures, even if they are not related to dislocation activity. In contrast to the recently proposed on-the-fly dislocation detection algorithm (ODDA) Stukowski (2010 Modelling Simul. Mater. Sci. Eng. 18 015012) the new method is extremely robust. While the ODDA was designed for a computationally efficient on-the-fly analysis, the DXA method enables a detailed analysis of dislocation lines even in highly distorted crystal regions, as they occur, for instance, close to grain boundaries or in dense dislocation networks.

Given two snapshots of an atomistic system, taken at different stages of the deformation process, one can compute the incremental deformation gradient field, F, as defined by continuum mechanics theory, from the displacements of atoms. However, such a kinematic analysis of the total deformation does not reveal the respective contributions of elastic and plastic deformation. We develop a practical technique to perform the multiplicative decomposition of the deformation field, F = F^eF^p, into elastic and plastic parts for the case of crystalline materials. The described computational analysis method can be used to quantify plastic deformation in a material due to crystal slip-based mechanisms in molecular dynamics and molecular statics simulations. The knowledge of the plastic deformation field, F^p, and its variation with time can provide insight into the number, motion and localization of relevant crystal defects such as dislocations. The computed elastic field, F^e, provides information about inhomogeneous lattice strains and lattice rotations induced by the presence of defects.

We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis algorithms such as common neighbor analysis (CNA), centrosymmetry analysis, bond angle analysis, bond order analysis and Voronoi analysis. In addition we propose a simple extension to the CNA method that makes it suitable for multi-phase systems. Finally, we introduce a new structure identification algorithm, the neighbor distance analysis, which is designed to identify atomic structure units in grain boundaries.

The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.

The objective of this work is to establish an analytical model for heat generation by friction stir welding (FSW), based on different assumptions of the contact condition between the rotating tool surface and the weld piece. The material flow and heat generation are characterized by the contact conditions at the interface, and are described as sliding, sticking or partial sliding/sticking. Different mechanisms of heat generation are behind each contact condition, making this study important for further understanding of the real FSW process. The analytical expression for the heat generation is a modification of previous analytical models known from the literature and accounts for both conical surfaces and different contact conditions. Experimental results on plunge force and torque are used to determine the contact condition. The sliding condition yields a proportional relationship between the plunge force and heat generation. This is not demonstrated in the experiment, which suggests that the sticking contact condition is present at the tool/matrix interface.

A new embedded-atom method (EAM) potential has been constructed for Ag by fitting to experimental and first-principles data. The potential accurately reproduces the lattice parameter, cohesive energy, elastic constants, phonon frequencies, thermal expansion, lattice-defect energies, as well as energies of alternate structures of Ag. Combining this potential with an existing EAM potential for Cu, a binary potential set for the Cu–Ag system has been constructed by fitting the cross-interaction function to first-principles energies of imaginary Cu–Ag compounds. Although properties used in the fit refer to the 0 K temperature (except for thermal expansion factors of pure Cu and Ag) and do not include liquid configurations, the potentials demonstrate good transferability to high-temperature properties. In particular, the entire Cu–Ag phase diagram calculated with the new potentials in conjunction with Monte Carlo simulations is in satisfactory agreement with experiment. This agreement suggests that EAM potentials accurately fit to 0 K properties can be capable of correctly predicting simple phase diagrams. Possible applications of the new potential set are outlined.

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.