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Additive manufacturing has enabled a transformational ability to create cellular structures (or foams) with tailored topology. Compared to their monolithic polymer counterparts, cellular structures are potentially suitable for systems requiring materials with high specific energy-absorbing capability to provide enhanced damping. In this work, we demonstrate the utility of controlling unit-cell topology with the intent of obtaining a desired stress-strain response and energy density. Using mesoscale simulations that resolve the unit-cell sub-structures, we validate the role of unit-cell topology in selectively activating a buckling mode and thereby modulating the characteristic stress-strain response. Simulations incorporate a linear viscoelastic constitutive model and a hyperelastic model for simulating large deformation of the polymer under both tension and compression. Simulated results for nine different cellular structures are compared with experimental data to gain insights into three different modes of buckling and the corresponding stress-strain response.

Understanding the phononic origin of the infrared dielectric properties of yttria (Y2O3) and other rare-earth sesquioxides (RE2O3) is a fundamental task in the search of appropriate RE2O3 materials that serve particular infrared optical applications. We herein investigate the infrared dielectric properties of RE2O3 (RE = Y, Gd, Ho, Lu) using DFT-based phonon calculations and Lorentz oscillator model. The abundant IR-active optical phonon modes that are available for effective absorption of photons result in high reflectance of RE2O3, among which four IR-active modes originated from large distortions of REO6 octahedra are found to contribute dominantly to the phonon dielectric constants. Particularly, the present calculation method by considering one-phonon absorption process is demonstrated with good reliability in predicting the infrared dielectric parameters of RE2O3 at the far-infrared as well as the vicinity of mid-infrared region, and the potential cutoff frequency/wavelength of its applicability is disclosed as characterized by the maximum frequency of IR-active longitudinal phonon modes. The results deepen the understanding on infrared dielectric properties of RE2O3, and aid the computational design of materials with appropriate infrared properties.

Anharmonic inter-atomic potential ∼ |x| ⁿ , n > 1 , has been used in
molecular dynamics (MD) simulations of stress dynamics of FCC oriented crystal.
The model of the chain of masses and springs is found as a convenient and accurate
description of simulation results, with masses representing the crystallographic planes.
The dynamics of oscillations of two planes is found analytically to be given by
Euler's beta functions, and its scaling with non-linearity parameter and amplitude
of oscillations, or applied shear pressure is discussed on examples of time dependencies
of displacements, velocities, and forces acting on masses (planes). The dynamics of
stress penetration from the surface of the sample with multiply-planes (an anharmonic
crystal) towards its interior is confirmed to be given exactly as a series of Bessel
functions, when n=2 (Schrödinger and Pater solutions). When n ̸= 2 the stress
dynamics (wave propagation) in bulk material remains qualitatively of the same nature
as in the harmonic case. In particular, results suggest that the quasi-linear relationship
between frequency and the wave number is preserved. The speed of the transverse
sound component, dependent on sound wave amplitude, is found to be a strongly
decreasing function of n. The results are useful in the analysis of any MD simulations
under pressure, as they help to understand the dynamics of pressure retarded effects,
as well as help design the proper methodology of performing MD simulations in cases
such as, for instance, studies of the dynamics of dislocations.

The current approach to modeling viscoelastic materials in most
commercial finite element packages is based on the General Maxwell Model, which
views these materials as combinations of spring and dashpot elements. However, the
data can be incorporated more directly into a transient finite element study by direct
interpolation of the relaxation function. This work explores a linear interpolation
scheme to the inclusion of viscoelastic relaxation functions on an example problem.
The results show several benefits over the General Maxwell Model for transient
studies. Included in the analysis are displacement solutions utilizing both approaches,
relaxation function error calculations for both approaches, and parametric runtime
studies comparing speed of calculation. The variation in computational flop counts is
considered and an argument is made for the preference of the proposed approach.

We examine the influence of grains size on the stability of polycrystalline coherent binary solid solutions. By assuming that the grains are isotropic, we find that the tendency for instability decreases as the radius of the grains decrease. We also find that a temperature-dependent critical grain radius exists below which the tendency for instability vanishes and the grains are stable, with respect to infinitesimal composition fluctuations, for any initial composition. We find that the critical grain radius decreases monotonically as the temperature decrease. If the radius of the grains is smaller than the minimum critical grain radius the grains are stable for any temperature and initial composition.

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.

The polycrystalline grain microstructure of metallic thin films coarsens during grain growth in a unique way when the initial grain structure contains multiple grains in the film thickness. A regime with fast coarsening is followed by a regime of slow coarsening. At the same time, the grain structure itself undergoes clear structural changes from a bulk-like to a bamboo-like structure. The overall coarsening process evolves continuously, whereas the growth paths of individual grains do not follow the ones observed and predicted in either two- or three-dimensional grain growth.

The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical properties of materials. However, the traditional approaches used to simulate grain boundaries lack physical fidelity and are often incompatible across different simulation methods. We review a new mesoscale interface boundary condition based on Burgers vector conservation and kinetic dislocation reaction processes. The main focus of the paper is to demonstrate how to unify this boundary condition with different plasticity simulation approaches such as the crystal plasticity finite element (CPFEM), continuum dislocation dynamics (CDD), and discrete dislocation dynamics (DDD) methods. In DDD and CDD, plasticity is simulated based on dislocation activity; in the former, dislocations are described as discrete lines while in the latter in terms of dislocation density. CPFEM simulates plasticity in terms of slip on each slip system, without explicit treatment of dislocations; it is suitable for larger scale simulations. To validate our interface boundary condition, we implemented simulations using both the CPFEM method and a two-dimensional CDD model. Our results show that our compact and physically realistic interface boundary condition can be easily integrated into multiscale simulation methods and yield novel results consistent with experimental observations.

Numerical simulations and optimizations methods are increasingly used in the field of kinetic analysis of solid-state processes, such as the crystallization of glassy materials. The influence of the simulations accuracy (with the two main factors being the initial value of conversion rate and the density of points) on the kinetic distortions was tested for the major solid-state kinetic models: nucleation-growth Johnson–Mehl–Avrami model, nth order reaction model, autocatalyzed nth order reaction model, diffusion models, contracting cylinder and contracting sphere models. The simulations were performed using a self-developed software based on the LSODA initial-value-problem-solver; the evaluation of the changes in the shape of the kinetic peaks was done using a commercial software that utilizes a standardized multivariate kinetic analysis approach. The accuracy was found to be influenced mainly by initial value of conversion rate. For majority of the tested kinetic models, the simulation accuracy had negligible effect on the consequently determined values activation energy, pre-exponential factor, integrated area of the kinetic peaks, or the asymmetry-determining values of the models kinetic exponents. Significant influence of the simulation accuracy was observed for the models with active autocatalytic features, which were identified to be the main source of the deviations introduced and propagated through the simulation algorithm. Contrary to the previous research, the deviations of the simulated peaks shape cannot be associated solely with the positive asymmetry of the kinetic peaks.

Lattice thermal conductivity plays an important role in material science, especially significant in thermoelectric materials. Recent research has unveiled the potential of high entropy alloys (HEAs) as good candidates for thermoelectric materials due to their notably low lattice thermal conductivity. This study investigates the lattice thermal conductivities of two specific HEAs, namely PbSnTeSe and PbSnTeS, through the application of molecular dynamics simulations (MDS) with machine-learned potentials. The findings not only demonstrate substantial agreement with experimental results for PbSnTeSe but also highlight the precision and efficiency of machine-learned potentials as a powerful tool in material research. The combination of machine-learned potentials with classical MDS offers an effective solution for simulating the thermodynamic properties of complicated systems like HEAs, with accuracy comparable to first-principle calculations. Furthermore, the investigation reveals that the lattice thermal conductivities of PbSnTeS are lower than those of PbSnTeSe, indicating its potential as a promising candidate for thermoelectric materials.

Understanding the effects of martensite volume fractions (V_m) in dual phase (DP) steel resulting from heat treatment is crucial for designing structures for mechanical impact resistance and optimizing manufacturing processes. DP steel's material behaviour depends heavily on its microstructure properties. While stress-strain curves for individual phases in DP steels are often determined using empirical models, extensive experimental data is required to establish empirical model constants. This research aims to achieve two main objectives: firstly, to calibrate stress-strain curves for pure ferrite and pure martensite using limited experimental data using micromechanical adaptive iteration algorithm (MAIA). This calibration involves using stress-strain data from DP steels with varying V_m during the calibration stage and additional data for verification. Secondly, to conduct a comprehensive sensitivity analysis of MAIA to assess its capabilities and limitations. Microstructure-based finite element (FE) models, simulated with ABAQUS/Standard, are employed to predict stress-strain curves under uniaxial tensile test conditions. The MAIA approach successfully calculated ferrite and martensite stress-strain curves that could predict plastic behaviour of DP steel with different V_m, which agreed with experimental work. Key advantages of this approach include avoiding complex 3D microstructure geometries and requiring only two experimentally obtained stress-strain curves with different Vm for material constant calibration, along with another curve for validation. However, the experimental data selected for calibration must have a V_m difference between 20%–50% and one of the DP steels must have a low martensite volume fraction. The FE micromechanical model could capture the effect of softening of martensite phase and strengthening of ferrite phase as compared to its bulk properties for DP steel. The effect of V_m on strain hardening rate was also successfully captured. This technique comes with obvious shortcomings, such as excluding crystal plasticity behaviour, and change in chemical composition within the individual phase with varying martensite volume fraction.