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Computationally modeling the laser powder bed fusion process can be expensive despite the fact that the laser covers a small fraction of the entire domain. Hence, we developed GO-MELT, a multilevel approach inspired by the variational multiscale method. GO-MELT calculates the full temperature solution using three coupled thermal solvers, each solving one of three overlapping domains, subsequently referred to as levels. Level 1's solver obtains a global, coarse-scale solution. Level 2's solver computes a meso-scale thermal field spanning the melt pool region. Level 3's solver obtains a fine-scale temperature field spanning the laser's immediate region. Coarser solutions provide boundary conditions for finer solvers. Finer solutions compute subgrid scales that influence coarser solvers through additional source terms. Being independently meshed, Levels 2 and 3 can track a laser along its tool path without remeshing. Moreover, fixed-sized, structured meshes allow for GPU acceleration using Google's JAX library with just-in-time compilation. Five case studies were conducted to demonstrate proper convergence of GO-MELT, to show that GO-MELT can reach the same accuracy as a uniform mesh with fewer degrees of freedom, and to quantify the computational load from each level's solver. A simulated production run averaged 1.64 ms per time step after taking 9.36 h to complete 20.5 million time steps, which is approximately 678 × faster than a uniform mesh solver with identical resolution and GPU acceleration. Future work will implement different solvers into GO-MELT to improve fidelity and speed. [Display omitted] • Developed multiscale framework inspired by VMS to combine separate thermal solvers. • Integrated GPU acceleration in Python using Google's JAX library with JIT compilation. • Simulated LPBF printing a 10 mm cube (20.5 million time steps) in 9.36 h. • Achieved 678x speedup compared to a uniform mesh of the same resolution. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) simulations offer an alternative to expensive AM experiments to study the effects of processing conditions on granular microstructures. Existing AM simulations lack support from reliable validation techniques. The stochastic nature and spatial heterogeneity of microstructures make it difficult to validate the simulated microstructures against experimentally obtained images through statistical measures such as average grain size. Another challenge is the lack of reliable and automated methods to calibrate the model parameters, which are unknown and difficult to measure directly from experiments. To overcome these two challenges, we first present a novel metric to quantify the difference between granular microstructures. Then, using this metric in conjunction with Bayesian optimization, we present a framework that can be used to reliably and efficiently calibrate the model parameters. We employ this framework to first calibrate the substrate microstructure simulation and then the laser scan microstructure simulation for Inconel 625. Results show that the framework allows successful calibration of the model parameters in just a small number of simulations. [ABSTRACT FROM AUTHOR]

Representative volume element (RVE)-based analysis plays a central role in understanding the response of heterogeneous materials to properties and geometry of the constituents. However, the accuracy of RVE analysis on real-life materials requires extra effort on the identification of material constituents and characterization of imperfections (e.g., voids and cracks) introduced in the fabrication process. For these reasons, together with the multiscale and spatially varying nature of heterogeneities, analysis of heterogeneous materials can be prohibitively time-consuming. In this work, a fully convolutional network (FCN)-based framework called RVE-net is proposed to take advantage of the state-of-art use of FCNs in image segmentation and feedforward neural networks in universal approximation to accelerate multiscale analysis, identify microscale material properties, and automatically characterize defects in materials. In contrast with standard numerical methods (e.g., the finite element method), which depend heavily on domain discretization and local interpolations, the RVE-net takes microstructure images — parameterized by a coupled Heaviside and level-set field representation — and loading conditions as inputs. The aim is to directly learn the nonlinear interaction between the microstructures and their local responses in a hierarchical manner. This avoids burdensome discretization and interpolations, makes it possible to transfer the learned structure-response from one microstructure to another, and thus significantly accelerates the modeling of heterogeneous materials. Several numerical examples are performed to examine the performance of the proposed RVE-net. It is demonstrated that the RVE-net can leverage the power of graphics processing units (GPUs) in RVE analysis, inverse derivation of material constituents, and characterization of defects. • Fully convolutional neural network, RVE-net, developed for feature-driven analysis. • RVE-net takes microstructure images and loading conditions as inputs. • Method allows simultaneous parametric study on both geometry and load conditions. • RVE-net can discover both quantities and fields of interest from external data. • RVE-net enables knowledge transfer from existing to new instances. [ABSTRACT FROM AUTHOR]

With growing application of additive manufacturing (AM) in industry, simulation of transient heat conduction during the AM process has drawn increasing attention. However, detailed simulation with acceptable accuracy is extremely time consuming because of the large range of time scales involved in the problem. In this work, a multi-time stepping method using different timesteps in multiple subdomains is developed to accelerate transient heat conduction simulation. A Dirichlet–Robin iterative coupling scheme is proposed to enforce continuity at the interfaces between different subdomains. This allows numerical stability of the multi-timestep​ model, even with disparate materials or meshes on either side of the subdomain interfaces. Specifically, an optimal approximation for the Schur complement matrix is derived using a one-dimensional (1D) model, which avoids the instabilities encountered when using a Dirichlet–Neumann coupling formulation and allows convergence of the iterative coupling scheme in only one iteration at each timestep. Several numerical examples are studied to evaluate the stability, convergence and performance of the method. It is found that the proposed method is robust and stable for all choices of material parameters, unlike the conventional Dirichlet–Neumann coupling scheme. To demonstrate the use of the method for AM, a simulation representative of a single laser track is performed and compared with line heat source model approach. It is found that the proposed method not only accelerates the simulation by a factor of more than 100, but gives very good accuracy for temperature in the melt pool region. • We present a multi-timestep, coupled domain method for transient heat conduction. • An optimal Robin coupling parameter is derived analytically. • The formulation is stable with disparate materials or mesh across the interface. • Multi-timestepping allows large acceleration with minimal loss of accuracy. [ABSTRACT FROM AUTHOR]

We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon. [Copyright &y& Elsevier]

The main objective of this paper is to develop a multiscale method for the analysis of carbon nanotube systems. The multiscale coupled governing equations are first derived based on a multiscale partition, which consists of a coarse scale component represented by meshfree approximation, and a fine scale component to be resolved from molecular dynamics. It is noted that the coarse scale representation is present in the entire domain of the problem, and coexists with the fine scale representation in the enriched region. Using the projection properties of the partition, the decoupled non-linear set of equations are obtained and solved iteratively using Newton''s method. In this multiscale analysis, a virtual atom cluster (VAC) model is also proposed in the coarse scale treatment. This model does not involve a stress update scheme employing the Cauchy–Born hypothesis, which has been widely used in the crystal elasticity theory. Finally, to approximate a curved surface at the nanoscale, meshfree approximations are introduced to interpolate a single layer of atoms. Unlike traditional shell or continuum elements, the geometric constraint is only imposed in two dimensions. The high order continuity property of the meshfree shape functions guarantees an accurate description of the geometry and thus the energy of the atomic bond. The accuracy and efficiency of the method are illustrated in the post-buckling analysis of carbon nanotube structures. To our knowledge, this is the first multiscale post-buckling analysis presented for such a nanoscale system. [Copyright &y& Elsevier]

We present a new method for coupling molecular dynamics (MD) and continuum mechanics simulations that is based on the projection of the MD solution onto the coarse scale shape functions. This projection, or “bridging scale”, represents that part of the solution that is obtainable by both solution methods. By subtracting the bridging scale from the total solution, we arrive at a coarse-fine decomposition that, by a proper choice of projection operator, decouples the kinetic energy of the two simulations. The resulting decomposition can be used in a finite-temperature simulation method in which MD is used only in a localized region, while the continuum simulation covers the entire domain, including the MD region to which it is coupled. One major advantage of this approach is that separate time step sizes can be used in the two simulations, so that the coarse scale time step is not limited to the time scale of the atomic vibrations present in the fine scale. Example problems are demonstrated on a 1D lattice, for which the method is shown to be accurate both for harmonic and anharmonic interatomic potentials. [Copyright &y& Elsevier]

In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A parallel computational implementation of a meshfree method—the reproducing kernel particle method (RKPM)—is used for 3-D implicit CFD analysis. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. Using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite-element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions. This technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations, many of which involve inherently serial steps; this is important, because the expense of meshfree computations makes parallelization crucial for large-size problems. The performance of the parallelization technique and the accuracy of the implicit CFD algorithm are demonstrated in two example problems. [Copyright &y& Elsevier]

Creation of new alloys through in-situ alloying in additive manufacturing is being actively explored to improve the properties and performance of manufactured parts. Multiphysics models are often used to investigate the underlying physics controlling AM processes using high-fidelity simulations of individual powder particle melting within the meltpool. In this paper, we present a novel multiphysics-multiphase model for simulating multicomponent powder beds during the AM process. A convection–diffusion formulation for component mass fraction, in conjunction with the Navier–Stokes equations and enthalpy form of the energy equation, enable us to predict the phase evolution in multicomponent beds and the dispersion of solute metals in the melt pool during the process. A non-equilibrium phase diagram (NEPD) model that incorporates the associated phase diagram is introduced to obtain the mass fraction in both solid and liquid phases as well as local temperature and liquid fraction by efficiently solving a set of nonlinear equations locally at each computational cell. This work introduces a numerical method for multicomponent Al-Zr binary material system for light-weight aluminum alloys, specifically demonstrating its efficacy and accuracy for eutectic solidification of this multicomponent. [ABSTRACT FROM AUTHOR]

In this article, the author refers to a study related to blood flow analysis of the aortic arch using computational fluid dynamics (CFD). It mentions that the researchers use patient-specific computer models of the thoracic aorta in combination with CFD. It states that echo cardiography and respiration-controlled 4D flow magnetic resonance imaging (MRI) enables assessment of cardiovascular haemodynamics in great vessels and the heart.

This paper presents a general Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN) computational framework for solving partial differential equations. This is the first paper of a series of papers devoted to C-HiDeNN. We focus on the theoretical foundation and formulation of the method. The C-HiDeNN framework provides a flexible way to construct high-order C n approximation with arbitrary convergence rates and automatic mesh adaptivity. By constraining the C-HiDeNN to build certain functions, it can be degenerated to a specification, the so-called convolution finite element method (C-FEM). The C-FEM will be presented in detail and used to study the numerical performance of the convolution approximation. The C-FEM combines the standard C 0 FE shape function and the meshfree-type radial basis interpolation. It has been demonstrated that the C-FEM can achieve arbitrary orders of smoothness and convergence rates by adjusting the different controlling parameters, such as the patch function dilation parameter and polynomial order, without increasing the degrees of freedom of the discretized systems, compared to FEM. We will also present the convolution tensor decomposition method under the reduced-order modeling setup. The proposed methods are expected to provide highly efficient solutions for extra-large scale problems while maintaining superior accuracy. The applications to transient heat transfer problems in additive manufacturing, topology optimization, GPU-based parallelization, and convolution isogeometric analysis have been discussed. [ABSTRACT FROM AUTHOR]

We propose the Convolution Hierarchical Deep-learning Neural Network (C-HiDeNN) that can be tuned to have superior accuracy, higher smoothness, and faster convergence rates like higher order finite element methods (FEM) while using only linear element's degrees of freedom. This is based on our newly developed convolution interpolation theory (Lu et al. in Comput Mech, 2023) and this article focuses on the deep-learning interpretation of C-HiDeNN with graphics processing unit (GPU) programming using JAX library in Python. Instead of increasing the degrees of freedom like higher order FEM, C-HiDeNN takes advantage of neighboring elements to construct the so-called convolution patch functions. The computational overhead of C-HiDeNN is reduced by GPU programming and the total solution time is brought down to the same order as commercial FEM software running on a CPU, however, with orders of magnitude better accuracy and faster convergence rates. C-HiDeNN is locking-free regardless of element types (even with 3-node triangular elements or 4-node tetrahedral elements). C-HiDeNN is also capable of r-h-p-mesh adaptivity like its predecessor HiDeNN (Zhang et al. in Comput Mech 67:207–230, 2021) with additional "a" (dilation parameter) adaptivity that stems from the convolution patch function and "p" adaptivity with higher accuracy and with the same degrees of freedom as that of the linear finite elements. C-HiDeNN potentially has myriad future applications in multiscale analysis, additive and advanced manufacturing process simulations, and high-resolution topology optimization. Details on these applications can be found in the companion papers (Lu et al. 2023; Saha et al. in Comput Mech, 2023; Li et al. in Comput Mech, 2023) published in this special issue. [ABSTRACT FROM AUTHOR]

We have measured the mechanical resonance of microscale quartz fibers to qualify the method of obtaining the Young’s modulus of nanowires from their resonance frequency and geometry. An equation for a circular beam with a linearly varying cross-section is derived and used to calculate the resonance frequency shift. We have established a model to discuss the boundary condition effect on the resonance frequency. The Young’s modulus of the quartz fibers has been determined by measuring the resonance frequency, and the geometry, and by applying the model that treats the influence of the type of clamp. The mean value from measurements of the fundamental resonance on 14 different microfibers is 70±6 GPa. This mean value is close to 72 GPa, the Young’s modulus of bulk fused quartz. Four resonance modes were observed in high vacuum and air. The mechanical resonance in high vacuum is linear at the fundamental vibration mode, and nonlinear for higher modes. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A three-dimensional molecular dynamics (MD) simulation is performed to study the stress generation mechanisms in carbon thin films grown by ion-beam deposition. The relationship between the kinetic energy of incident ions and the steady-state film stress is established. Examination of the atomic stress and film microstructures reveals that the grown films contain a significant fraction of vacancies, contradicting the presumption of the subplantation model. By taking into account both interstitials and vacancies, an analytical model is developed, in which the formation of the compressive stress is attributed to competing mechanisms between generation and recovery of the defects. This model can satisfactorily explain the numerical observation in which compressive stress prevails in films in the presence of vacancies. The present study provides useful insights into tailoring residual stress to control thin film curvature in microelectromechanical systems (MEMS) by ion-beam machining. [Copyright &y& Elsevier]

We are witnessing a rapid transition from Software 1.0 to 2.0. Software 1.0 focuses on manually designed algorithms, while Software 2.0 leverages data and machine learning algorithms (or artificial intelligence) for optimized, fast, and accurate solutions. For the past few years, we have been developing Convolution Hierarchical Deep-learning Neural Network Artificial Intelligence (C-HiDeNN-AI), which enables the realization of Engineering Software 2.0 by opening the next-generation neural network-based computational tools that can simultaneously train data and solve mechanistic equations. This paper focuses on solving partial differential equations with C-HiDeNN. Still, the same neural network can be used for training and calibration with experimental data, which will be discussed in a separate paper. This paper presents a computational framework combining the C-HiDeNN theory with isogeometric analysis (IGA), called Convolution IGA (C-IGA). C-IGA has five key features that advance IGA: (1) arbitrarily high-order smoothness and convergence rates without increasing degrees of freedom; (2) a Kronecker delta property that enables direct imposition of Dirichlet boundary conditions; (3) automatic and flexible global/local mesh-adaptivity with built-in length scale control and adjustable radial basis functions; (4) ability to handle irregular meshes and triangular/tetrahedral elements; and (5) GPU implementation that speeds up the program as fast as finite element method (FEM). Mathematically, we prove that both IGA and C-IGA mappings are equivalent, and by taking a special design and modified anchors as nodes, C-IGA degenerates to IGA. We demonstrate the accuracy, convergence rates, mesh-adaptivity, and performance of C-IGA with several 1D, 2D, and 3D numerical examples. The future applications of C-IGA from topology optimization to product manufacturing with multi-GPU programming are discussed. [ABSTRACT FROM AUTHOR]

Metal powder-based Additive Manufacturing (AM) processes are increasingly used in industry and science due to their unique capability of building complex geometries. However, the immense computational cost associated with AM predictive models hinders the further industrial adoption of these technologies for time-sensitive applications, process design with uncertainties or real-time process control. In this work, a novel approach to accelerate the explicit finite element analysis of the transient heat transfer of AM processes is proposed using Graphical Processing Units. The challenges associated with this approach are enumerated and multiple strategies to overcome each challenge are discussed. The performance of the proposed algorithms is evaluated on multiple test cases. Speed-ups of about 100 ×–150 × compared to an optimized single CPU core implementation for the best strategy were achieved. [ABSTRACT FROM AUTHOR]

Abstract The level set method for modeling multi-fluid interfaces gives a simple approach for the simulation of multiphase flow problems. However, many of the components of this method, such as the redistancing of the level set function and discretization of the singular surface tension force, become more difficult on unstructured meshes in a control volume framework; furthermore, these operations are shown to lead to errors in conservation of mass of the individual phases, as well as unphysical currents near the interface. This paper presents a novel formulation for the level set method combined with a balanced-force algorithm using a control volume finite element method (CVFEM) for unstructured grids. A diffuse interface description is used, allowing a straightforward inclusion of surface tension forces; we show that by consistently evaluating the pressure gradient and surface tension, we are able to discretely balance these two forces and suppress any parasitic currents given a prescribed curvature. By converting the redistancing equation to a form that is suitable for CVFEM and enforcing a constraint directly linked with the phase fraction in each cell, we are able conserve mass and preserve the shape of the interface to a high degree of accuracy in multiphase flow problems with high density and viscosity ratios. The accuracy of the of our proposed method is assessed by comparing with benchmark results from the literature. Highlights • A novel level set formulation utilizing CVFEM is proposed. • A balanced-force algorithm is formulated for purely unstructured meshes. • The redistancing equation is reformulated to allow higher order upwinding methods. • A new constraint is introduced to preserve the shape of the interface. • Benchmark examples show convergence for high density and viscosity ratio problems. [ABSTRACT FROM AUTHOR]

One goal of modeling for metal Additive Manufacturing (AM) is to predict the resultant mechanical properties from given manufacturing process parameters and intrinsic material properties, thereby reducing uncertainty in the material built. This can dramatically reduce the time and cost for the development of new products using AM. We have realized the seamless linking of models for the manufacturing process, material structure formation, and mechanical response through an integrated multi-physics modeling framework. The sequentially coupled modeling framework relies on the concept that the results from each model used in the framework are contained in space-filling volume elements using a prescribed structure. This framework is implemented to show a prediction of the decrease in fatigue life caused by insufficient fusion resulting from low laser power relative to the hatch spacing. In this demonstration, powder spreading and thermal-fluid flow models are used to predict the thermal history and void formation in a multilayer, multi-track build with different processing conditions. The results of these predictions are passed to a cellular automaton-based prediction of grain structure. Finally, the predicted grain and void structure is passed to a reduced-order micromechanics-based model to predict mechanical properties and fatigue life arising from the different processing conditions used in the process model. The simulation results from this combination of models demonstrate qualitative agreement with experimental observations from literature, showing the appealing potential of an integrated framework. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) possesses appealing potential for manipulating material compositions, structures and properties in end-use products with arbitrary shapes without the need for specialized tooling. Since the physical process is difficult to experimentally measure, numerical modeling is a powerful tool to understand the underlying physical mechanisms. This paper presents our latest work in this regard based on comprehensive material modeling of process-structure-property relationships for AM materials. The numerous influencing factors that emerge from the AM process motivate the need for novel rapid design and optimization approaches. For this, we propose data-mining as an effective solution. Such methods—used in the process-structure, structure-properties and the design phase that connects them—would allow for a design loop for AM processing and materials. We hope this article will provide a road map to enable AM fundamental understanding for the monitoring and advanced diagnostics of AM processing. [ABSTRACT FROM AUTHOR]

In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments. [ABSTRACT FROM AUTHOR]

Selective Electron Beam Melting (SEBM) is a promising powder-based metallic Additive Manufacturing (AM) technology. However, most powder-scale modeling efforts are limited to single track process, while it is also difficult to experimentally observe the interaction between tracks and layers. In this study, we develop an integrated modeling framework to investigate the SEBM process of multiple tracks and multiple layers. This approach consists of a Discrete Element model of powder spreading and a Computational Fluid Dynamics (CFD) model of powder melting. These two models exchange 3D geometrical data as a cycle to reproduce the manufacturing process of multiple tracks along various scan paths in multiple powder layers. This integrated modeling approach enables further understanding of how current tracks and layers interact with previous ones leading to inter-track/layer voids. It also incorporates more influential factors, particularly the layer-wise scan strategy. The inter-layer/track voids due to the lack of fusion are systematically discussed in light of our simulation results which qualitatively agree with experimental observations in literature. [ABSTRACT FROM AUTHOR]

Metallic powder bed-based additive manufacturing technologies have many promising attributes. The single track acts as one fundamental building unit, which largely influences the final product quality such as the surface roughness and dimensional accuracy. A high-fidelity powder-scale model is developed to predict the detailed formation processes of single/multiple-track defects, including the balling effect, single track nonuniformity and inter-track voids. These processes are difficult to observe in experiments; previous studies have proposed different or even conflicting explanations. Our study clarifies the underlying formation mechanisms, reveals the influence of key factors, and guides the improvement of fabrication quality of single tracks. Additionally, the manufacturing processes of multiple tracks along S/Z-shaped scan paths with various hatching distance are simulated to further understand the defects in complex structures. The simulations demonstrate that the hatching distance should be no larger than the width of the remelted region within the substrate rather than the width of the melted region within the powder layer. Thus, single track simulations can provide valuable insight for complex structures. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) of titanium alloys is a rapidly growing field due to an increase in design flexibility of parts. However, AM parts are highly anisotropic in material microstructure and mechanical behavior due to the change of the local processing conditions in the build-up process. This study follows a link chain model to investigate the relationships between process parameters, cooling rate, porosity and mechanical behavior. The aim of this work is to present a framework that is inspired by the three-link chain model. The framework combines theoretical, computational and experimental approaches. We demonstrate this by using an in-house thermal simulator to link predicted cooling rates with micrographs describing experimental shape descriptors to develop a relationship between solidification cooling rate and porosity geometry. Finally, representative volume elements from predicted porosity maps allow for a prediction of mechanical properties at localized areas. The capability of being able to predict mechanical behavior of titanium alloys is demonstrated for the directed energy deposition process. [ABSTRACT FROM AUTHOR]

A concurrent multiscale method is developed to model time-dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved. Ensuring this energetic consistency among scales enables the implementation of high fidelity physics-based models at critical locations within the coarse-scale to temporally and spatially resolve highly complex and localized phenomena. To achieve this, only Neumann boundary conditions are applied over the fine scale domain, ensuring a conservative formulation. The coarse-scale solution is used to reconstruct these Neumann boundary conditions on the fine scale, which are then used to evolve a separate system of governing equations. The results on the fine scale are then sent back to the coarse scale through an energy-based homogenization scheme. Transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness, including the coupling of a phase field model at the fine scale to a coarse-scale heat equation. [ABSTRACT FROM AUTHOR]

This paper presents an in-depth numerical analysis of spatial fractional advection–diffusion equations (FADE) utilizing the finite element method (FEM). A traditional Galerkin finite element formulation of the pure fractional diffusion equation without advection may yield numerical oscillations in the solution depending on the fractional derivative order. These oscillations are similar to those that may arise in the integer-order advection–diffusion equation when using the Galerkin FEM. In a Galerkin formulation of a FADE, these oscillations are further compounded by the presence of the advection term, which we show can be characterized by a fractional element Peclet number that takes into account the fractional order of the diffusion term. To address this oscillatory behavior, a Petrov–Galerkin method is formulated using a fractional stabilization parameter to eliminate the oscillatory behavior arising from both the fractional diffusion and advection terms. A compact formula for an optimal fractional stabilization parameter is developed through a minimization of the residual of the nodal solution. Steady state and transient one-dimensional cases of the pure fractional diffusion and fractional advection–diffusion equations are implemented to demonstrate the effectiveness and accuracy of the proposed formulation. [ABSTRACT FROM AUTHOR]

Directed energy deposition (DED) is an advanced additive manufacturing technology for the fabrication of near-net-shape metal parts with complex geometries and high performance metrics. Studying the grain structure evolution during the process is pivotal to evaluating and tailoring the as-built products' mechanical properties. However, it is time-consuming to simulate the multi-layer deposition process using the physics-based numerical model to optimize the process parameters for achieving the desired microstructure. In this paper, a physics-informed machine learning algorithm to predict the grain structure in the DED process is proposed. To generate training data for the machine learning algorithm, we use an experimentally validated cellular automaton finite volume method (CAFVM) for DED Inconel 718, where CA is applied to model the grain structure and FVM to simulate the heat transfer. We develop a neural network model to identify the correlation between the local thermal features and their corresponding grain structure characteristics. The inputs and outputs of the neural network (NN) model are selected based on the governing physics, and a novel way to extract them is proposed. The NN model can quickly predict the grain structure characteristics with the local thermal data for thin-wall builds, and the predictions are in good agreement with the numerical simulation results. We expect the proposed method can benefit other metal additive manufacturing technologies to formulate efficient and accurate process-structure relationships and in-process feedback control. [Display omitted] • Predict additively manufactured grain structure with a machine learning method. • An 3D cellular automaton finite volume method for "the ground truth" microstructure. • Strategy to represent the grain size and aspect ratio variation in a neural network. • Simulated thin-wall builds of Inconel 718 by directed energy deposition. [ABSTRACT FROM AUTHOR]

A well characterized and predictable aging pattern is necessary for practical energy storage applications of nanoporous particles that facilitate rapid transport of ions or redox species. Here we use STEM tomography with segmentation to show that surface diffusion and grain boundary diffusion are responsible for pore evolution at intermediate and higher temperatures, respectively. This unprecedented three dimensional understanding of pore behavior as a function of temperature suggests routes for optimizing pore stability in future energy storage materials. [ABSTRACT FROM AUTHOR]

Abstract: Inspired by the pioneering work of Professor T.J.R. Hughes on the variational multi-scale method, this document summarizes recent developments in multiple-scale modeling using a newly developed technique called the bridging scale. The bridging scale consists of a two-scale decomposition in which the coarse scale is simulated using continuum methods, while the fine scale is simulated using atomistic approaches. The bridging scale offers unique advantages in that the coarse and fine scales evolve on separate time scales, while the high frequency waves emitted from the fine scale are eliminated using lattice impedance techniques. Recent advances in extending the bridging scale to quantum mechanical/continuum coupling are briefly described. The method capabilities are demonstrated via quasistatic nanotube bending, dynamic crack propagation and dynamic shear banding. [Copyright &y& Elsevier]

Single crystals of KPb2Cl5 were grown by vertical Bridgman technique from purified and synthesized material doped with Erbium up to a concentration of 5 mol% ErCl3. The purification was performed by zone refining at a rate of 3 cm/hr for 30 passes, with a final refining at a rate of 1 mm/hr. Segregation coefficient of Er3+ ions was found to be ∼0.5 for KPb2Cl5. The transmission through a 12-mm thick crystal was found to be ∼80%, the mid-infrared and visible up-conversion luminescence spectra are reported. [Copyright &y& Elsevier]

Additive manufacturing (AM) is an emerging technology that fuses deposited powder materials together layer-by-layer using a localized heat source to create an arbitrarily complex geometry. This technology is an inherently multiphysics problem, involving the simultaneous evolution of fluid flow, heat transfer, free surface, laser-material interaction and material phases including solid, liquid and gas. Multiphysics and multiphase models are typically used to understand the dominant physics driving AM processes through high fidelity simulations resolving the individual powders as they melt onto the substrate. However, these types of high fidelity models have not been applicable to modeling directed energy deposition (DED) process, where powders are delivered through the ambient vapor onto the substrate by a nozzle and subsequently fused. This paper presents a novel multiphase thermo-fluid formulation for modeling DED processes. A diffuse level set formulation coupled with the Navier–Stokes, energy conservation and radiative transport equation allows us to model complex free surface, fluid flow, thermal and laser interaction evolution. In addition, our formulation enables us to resolve the vapor flow field and its effect on deposited material during AM processes. The accuracy of our proposed method is assessed by comparing with literature solutions and experimental benchmarks. Our proposed formulation is then used to model simple DED processes that enable us to visualize the entrainment of powder particles into the melt pool. This process elucidates the dominant physical forces that can drive powders into the melt pool as well as their effect on the melt pool evolution within DED processes. • A novel formulation is proposed to model solid–liquid–vapor flow with phase change. • Conservative level set and balanced force algorithm allow robust treatment of moving interfaces. • Controlled benchmark experiments validate the proposed model. • Directed energy deposition simulations elucidate particle entrainment effects. [ABSTRACT FROM AUTHOR]

Abstract Additive manufacturing (AM) processes produce unique microstructures compared with other manufacturing processes because of the large thermal gradient, high solidification rate and other local temperature variations caused by the repeated heating and melting. However, the effect of these thermal profiles on the microstructure is not thoroughly understood. In this work, a 3D cellular automaton method is coupled to a finite volume method to predict the grain structure of an alloy, e.g. Inconel 718, fabricated by AM. The heat convection due to thermocapillary flow inside the melt pool is resolved by the finite volume method for a real and accurate temperature field, while an enriched grain nucleation scheme is implemented to capture epitaxial grain growth following the mechanism identified from experiments. Simulated microstructure results are shown to be in qualitative agreement with experimental result and the effects of the process parameters on both thermal characteristics and the grain structure are identified. The 3D cellular automaton finite volume method results establish our approach as a powerful technique to model grain evolution for AM and to address the process-structure-property relationship. Graphical Abstract Unlabelled Image Highlights • A 3D cellular automata finite volume method for additive manufacturing is presented, including an enriched nucleation model • The grain structure in the Directed Energy Deposition of IN718 alloy is simulated by the proposed method • The effects of the processing parameters on the resulting grain structure of IN718 alloy are elaborated via the simulation • Sandwich- and zig-zag patterns of grain structure observed in experiments are captured and explained by the proposed model [ABSTRACT FROM AUTHOR]