Modelling and Simulation in Materials Science and Engineering

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.

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.

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/.

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.

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.

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.

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.

Density functional theory (DFT) codes are commonly treated as a 'black box' in high-throughput screening of materials, with users opting for the default values of the input parameters. Often, non-experts may not sufficiently consider the effect of these parameters on prediction quality. In this work, we attempt to identify a robust set of parameters related to smearing and tetrahedron methods that return numerically accurate and efficient results for a wide variety of metallic systems. The effects of smearing and tetrahedron methods on the total energy, number of self-consistent field cycles, and forces on atoms are studied in two popular DFT codes: the Vienna ab initio Simulation Package and Quantum Espresso. From nearly 40 000 computations, it is apparent that the optimal smearing depends on the system, smearing method, smearing parameter, and k-point density. The benefit of smearing is a minor reduction in the number of self-consistent field cycles, which is independent of the smearing method or parameter. A large smearing parameter—what is considered large is system dependent—leads to inaccurate total energies and forces. Blöchl's tetrahedron method leads to small improvements in total energies. When treating diverse systems with the same input parameters, we suggest using as little smearing as possible due to the system dependence of smearing and the risk of selecting a parameter that gives inaccurate energies and forces.

This work addresses in-situ synergistic irradiation and thermomechanical loading of nuclear reactor components by linking new mechanistic understanding with crystal plasticity finite element modelling to describe the formation and thermal and mechanical annihilation of dislocation loops. A model of pressurised reactor cladding is constructed to extract realistic boundary conditions for crystal plasticity microstructural sub-modelling. Thermomechanical loads are applied to the sub-model to investigate (i) the unirradiated state, (ii) synergistic coupling of irradiation damage and thermal annihilation of dislocation loops, (iii) synergistic coupling of irradiation damage without thermal annihilation of dislocation loops, and (iv) a post-irradiated state. Results demonstrate that the synergistic coupling of irradiation damage and thermomechanical loads leads to the early onset of plasticity, which is exacerbated by the thermal annihilation of dislocations, while the post-irradiated case remains predominantly elastic due to substantial irradiation hardening. It is shown that full synergistic coupling leads to localisation of quantities linked with crack nucleation including geometrically necessary dislocations and stress.

We present a mechano-chemical model that couples corrosion, mechanical response, and fracture. The model is used to understand the failure of Cu wires on Al pads in microelectronic packages using a multi-phase field approach. Under high humidity environments, the Cu-rich intermetallic compounds (IMC), Cu₉Al₄, formed at the interface between Cu and Al, undergo a corrosion degradation process. The IMC expands while undergoing corrosion, inducing stresses that nucleate and propagate cracks along the interface between the Cu-rich IMC and Cu. Furthermore, the volumetric expansion of the IMC may cause damage to the passivation layer and enhance the nucleation of new corrosion pits. We show that the presence of a crack accelerates the corrosion process. The model developed here can be extended to other systems and applications.

In order to investigate the nanoscale friction mechanism and deformation behavior of nickel-copper bilayer film under rolling scraping, the effects of different factors during friction process such as the translation velocity, rotation velocity, radius of abrasive grain, contact depth, texture direction and crystallographic orientation are analyzed through molecular dynamics methods in terms of contact force, atomic lattice structure, internal substrate dislocation, kinetic energy and temperature. Results show that the contact force increases with the increase of the translation velocity or the decrease of the rotation velocity. Abrasive grains in a purely rolling state cause the most serious damage to the substrate. The contact force increases with the increase of contact depth or the decrease of abrasive grain radius. The crystallographic orientation has a significant effect on rolling scraping process and there is a crystallographic orientation with the minimum contact force. The degrees of substrate dislocation and the numbers of lattice reconstruction atoms under different factors and levels vary widely.

This work presents a dislocation density-based crystal plasticity constitutive model for glide kinetics, strengthening and dislocation density evolution, implemented in the effective medium-based visco-plastic self consistent (VPSC) framework and the spatially resolved, ρ-CP crystal plasticity finite element framework. Additionally, a distribution of intragranular stresses is introduced in the VPSC framework, instead of the conventionally used mean value of grain stress for effective medium calculations. The ρ-CP model is first calibrated to predict the mechanical response of a bcc ferritic steel with an initial rolled texture. The same set of constitutive model parameters are then used in VPSC to predict the aggregate stress–strain response and total dislocation densities. For these VPSC simulations, the interaction parameter governing the interaction between the grain and the effective medium in the Eshelby inclusion formalism, and a scalar parameter representative of the distribution of intragranular stresses within a grain, are used to calibrate the VPSC predictions in order to match the predictions of the ρ-CP model. A parametric study is performed to understand the effect of these two parameters on the VPSC predictions. Further, simulations are also performed for a random untextured polycrystal to identify the corresponding VPSC simulation parameters for predicting a similar response as the ρ-CP model. The novelty of the work is in the same set of constitutive models and associated parameters have been implemented in VPSC and ρ-CP to predict similar aggregate stress–strain response and total dislocation densities. This finite element-calibrated effective medium crystal plasticity approach reduces the computational time by at least two orders of magnitude and represents an advance towards the development of multiscale crystal plasticity modeling tools.

Diamond, possessing high hardness and chemical stability, finds wide-ranging applications across various industries. However, during the friction process, a graphitization phenomenon may occur, which changes the mechanical properties of the diamond. In this study, molecular dynamics simulation was performed using SiC ball to investigate the influence of indentation depth and temperature on the graphitization transition of the diamond surface. The results showed that the dominant factor affecting the sp² hybridization ratio during the indentation process was stress, while the temperature was the dominant factor during sliding. The results of this study can be used to understand the friction and wear behavior of diamonds and SiC ball and provide theoretical references for the industrial application of diamonds.

This study uses molecular dynamics simulations to explore the mechanical properties of a nano-twinned copper–nickel alloy during indentation. We investigate the impact of twin boundary (TB) angles and spacing on the alloy's behavior. The plastic deformation process is primarily driven by dislocation generations, slips, and TB interactions, directly affecting the alloy's hardness. Significant findings include: (1) hardness initially decreases, then increases with increasing TB angle θ, and for TB spacing d greater than 1.25 nm, hardness can be predicted using a simple proposed model; (2) dislocation density ρ experiences significant variations, leveling off at an indentation depth around 1.0 nm; (3) when TB spacing d exceeds 1.25 nm, plastic deformation is dominated by dislocation nucleation, slips, and boundary interactions, while smaller spacings lead to TB migration and the presence of independent dislocation loops, giving rise to force fluctuations along indentation.

Semi-coherent interfaces can have a strong influence on the mechanical behavior of bilayer systems, which is seen very clearly under indentation conditions where a well-defined plastic zone interacts directly with the interface. The main aim of this work is to study the influence of a semi-coherent bcc/bcc interface in the V/Fe bilayer system with molecular dynamics (MD) simulations. In particular, the influence of the V layer thicknesses on the apparent hardness of bilayer system is investigated. Our results show that the deformation behavior of pure V and pure Fe resulting from the MD simulations is in good agreement with the literature. Moreover, the MD simulations reveal a significant enhancement of the hardness of V/Fe bilayer system for thinner vanadium layers, resulting from the crucial role of the semi-coherent interface as a barrier to dislocation propagation. This is seen from a detailed analysis of the interaction of mobile dislocations in the plastic zone with misfit dislocations in the interface. Our work shows that dislocation pile-ups at the interface and formation of horizontal shear loops are two key mechanisms dominating the rate and magnitude of plastic deformation and thus contributes to our understanding of mechanical behavior of bilayer systems with semi-coherent interfaces.

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.

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.

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.

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.

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.

The Swift-Hohenberg (SH) and Phase-Field Crystal (PFC) models are minimal yet powerful approaches for studying phenomena such as pattern formation, collective order, and defects via smooth order parameters. They are based on a free-energy functional that inherently includes elasticity effects. This study addresses how gradient elasticity (GE), a theory that accounts for elasticity effects at microscopic scales by introducing additional characteristic lengths, is incorporated into SH and PFC models. After presenting the fundamentals of these theories and models, we first calculate the characteristic lengths for various lattice symmetries in an approximated setting. We then discuss numerical simulations of stress fields at dislocations and comparisons with analytic solutions within first and second strain-gradient elasticity. Effective GE characteristic lengths for the elastic fields induced by dislocations are found to depend on the free-energy parameters in the same manner as the phase correlation length, thus unveiling how they change with the quenching depth. The findings presented in this study enable a thorough discussion and analysis of small-scale elasticity effects in pattern formation and crystalline systems using SH and PFC models and, importantly, complete the elasticity analysis therein. Additionally, we provide a microscopic foundation for GE in the context of order-disorder phase transitions.

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.

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.

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.

This work addresses in-situ synergistic irradiation and thermomechanical loading of nuclear reactor components by linking new mechanistic understanding with crystal plasticity finite element modelling to describe the formation and thermal and mechanical annihilation of dislocation loops. A model of pressurised reactor cladding is constructed to extract realistic boundary conditions for crystal plasticity microstructural sub-modelling. Thermomechanical loads are applied to the sub-model to investigate (i) the unirradiated state, (ii) synergistic coupling of irradiation damage and thermal annihilation of dislocation loops, (iii) synergistic coupling of irradiation damage without thermal annihilation of dislocation loops, and (iv) a post-irradiated state. Results demonstrate that the synergistic coupling of irradiation damage and thermomechanical loads leads to the early onset of plasticity, which is exacerbated by the thermal annihilation of dislocations, while the post-irradiated case remains predominantly elastic due to substantial irradiation hardening. It is shown that full synergistic coupling leads to localisation of quantities linked with crack nucleation including geometrically necessary dislocations and stress.

Non-woven cellulose fiber networks of low areal density are widely used in many industrial applications and consumer products. A discrete element method (DEM) modeling framework is advanced to simulate the formation of strongly anisotropic cellulose fiber network sheets in the dilute limit with simplified hydrodynamic and hydroelastic interactions. Our modeling accounts for in-plane fiber orientation and viscous drag indirectly by using theories developed by Niskanen (2018 Fundamentals of Papermaking, Trans. 9th Pulp and Paper Fundamental Research Symp. Cambridge, 1989 (FRC) pp 275–308) and Cox (1970 J. Fluid Mech.44 791–810) respectively. Networks formed on a patterned and flat substrate are simulated for different fiber types, and their tensile response is used to assess the influence of the out-of-plane topographical pattern, specifically, on their stiffness and strength. Sheets with the same grammage and thickness, but composed with a higher fraction of softwood fiber (longer fibers with large diameter), have higher strength and higher strain to failure compared to sheets made from hardwood fibers (short fibers with small diameter). However, varying the fiber fraction produces only an insignificant variation in the initial sheet stiffness. The above simulation predictions are confirmed experimentally for sheets comprised of fibers with different ratios of Eucalyptus kraft and Northern Bleached Softwood Kraft fibers. Sheets with out-of-plane topography show an unsymmetric mass distribution, lower tensile stiffness, and lower tensile strength compared to those formed on a flat substrate. The additional fiber deformation modes activated by the out-of-plane topography, such as bending and twisting, explain these differences in the sheet mechanical characteristics.

We present a mechano-chemical model that couples corrosion, mechanical response, and fracture. The model is used to understand the failure of Cu wires on Al pads in microelectronic packages using a multi-phase field approach. Under high humidity environments, the Cu-rich intermetallic compounds (IMC), Cu₉Al₄, formed at the interface between Cu and Al, undergo a corrosion degradation process. The IMC expands while undergoing corrosion, inducing stresses that nucleate and propagate cracks along the interface between the Cu-rich IMC and Cu. Furthermore, the volumetric expansion of the IMC may cause damage to the passivation layer and enhance the nucleation of new corrosion pits. We show that the presence of a crack accelerates the corrosion process. The model developed here can be extended to other systems and applications.

We present OpenPFC (https://github.com/VTT-ProperTune/OpenPFC), a state-of-the-art phase field crystal (PFC) simulation platform designed to be scalable for massive high-performance computation environments. OpenPFC can efficiently handle large-scale simulations, as demonstrated by our strong and weak scaling analyses up to an 8192³ grid on 65 536 cores. Our results indicate that meaningful PFC simulations can be conducted on grids of size 2048³ or even 4096³, provided there is a sufficient number of cores and ample disk storage available. In addition, we introduce an efficient implementation of moving boundary conditions that eliminates the need for copying field values between MPI processes or adding an advection term to the evolution equations. This scheme enhances the computational efficiency in simulating large scale processes such as long directional solidification. To showcase the robustness of OpenPFC, we apply it to simulations of rapid solidification in the regime of metal additive manufacturing using a recently developed quantitative solid-liquid-vapor PFC model, parametrized for pure tungsten (body-centered cubic) and aluminum (face-centered cubic).

A new machine-learning interatomic potential, specifically a moment tensor potential (MTP), is developed for the study of screw-dislocation properties in body-centered-cubic (bcc) Nb in the thermally- and stress-assisted temperature regime. Importantly, configurations with straight screw dislocations and with kink pairs are included in the training set. The resulting MTP reproduces with near density-functional theory (DFT) accuracy a broad range of physical properties of bcc Nb, in particular, the Peierls barrier and the compact screw-dislocation core structure. Moreover, it accurately reproduces the energy of the easy core and the twinning-anti-twinning asymmetry of the critical resolved shear stress (CRSS). Thereby, the developed MTP enables large-scale molecular dynamics simulations with near DFT accuracy of properties such as for example the Peierls stress, the critical waiting time for the onset of screw dislocation movement, atomic trajectories of screw dislocation migration, as well as the temperature dependence of the CRSS. A critical assessment of previous results obtained with classical embedded atom method potentials thus becomes possible.

Despite the existence of time domain finite element formulations for viscoelastic materials, there are still substantial ways to improve the analysis. To the authors' knowledge, the formulation of the problem is always done with respect to a single constitutive relation and so limits the implementer to a single scheme with which to model relaxation. Furthermore, all current constitutive relations involve the finding of fitting parameters for an analytical function, which is a sufficiently painful process to warrant the study of best fitting procedures to this day. In contrast, this effort is the first full derivation of the two dimensional problem from fundamental principles. It is also the first generalization of the problem, which frees users to select constitutive relations without re-derivation or re-expression of the problem. This approach is also the first approach to the problem that could lead to the elimination of constitutive relations for representing relaxation in viscoelastic materials. Following, the full derivation, several common constitutive relations are outlined with analysis of how they may best be implemented in the generalized form. Several expressions for viscoelastic terms are also provided given linear, quadratic, and exponential interpolation assumptions.