Search

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]

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]

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]

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]

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]

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]

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]

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]