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Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element $$\mathcal {RVE}$$ RVE . The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model.

Advancements in additive manufacturing (3D printing) have enabled researchers to create complex structures, offering a new class of materials that can surpass their individual constituent properties. Selective laser sintering (SLS) is one of the most popular additive manufacturing techniques and uses laser power to bond powdered material into intricate structures. It is one of the fastest additive manufacturing processes for printing functional, durable prototypes, or end-user parts. It is also widely used in many industries, due to its ability to easily make complex geometries with little to no additional manufacturing effort. In the SLS process, tool path selection is important because it is directly related to the integrity of a 3D printed structure. In this research, we focus on how to obtain an optimal tool path for the SLS process from a numerical simulation. Also, we apply a deep learning technique to accelerate the simulation of the SLS processes, while obtaining accurate numerical results.

This work develops a computational Digital-Twin framework to track and optimize the flow of solar power through complex, multipurpose, solar farm facilities, such as Agrophotovoltaic (APV) systems. APV systems symbiotically cohabitate power-generation facilities and agricultural production systems. In this work, solar power flow is rapidly computed with a reduced order model of Maxwell’s equations, based on a high-frequency decomposition of the irradiance into multiple rays, which are propagated forward in time to ascertain multiple reflections and absorption for various source-system configurations, varying multi-panel inclination, panel refractive indices, sizes, shapes, heights, ground refractive properties, etc. The method allows for a solar installation to be tested from multiple source directions quickly and uses a genomic-based Machine-Learning Algorithm to optimize the system. This is particularly useful for planning of complex next-generation solar farm systems involving bifacial (double-sided) panelling, which are capable of capturing ground albedo reflection, exemplified by APV systems. Numerical examples are provided to illustrate the results, with the overall goal being to provide a computational framework to rapidly design and deploy complex APV systems.

Shotguns have increasingly used case-hardened steel pellets, as opposed to “classical” lead, owing to food safety and environmental concerns. Correspondingly, there is increasing concern about unintended ricochet of pellets and subsequent bodily harm, such as eye damage. Correspondingly, this paper focuses on the impact of pellets with a surface and the post-impact ricochet range. Equations for general three-dimensional inelastic impact with unilateral stick–slip conditions are derived for pellets and a post-impact trajectory analysis is performed. Qualitatively, with increasing friction, ranges of ricochet decrease because most of the pre-impact translational energy of the pellets is converted upon impact into rotational energy, which reduces the post-impact ricochet range. For slippery surfaces, wide ranging trajectory distributions occur owing to the mix of stick and slip conditions among the pellets. In the case of slip, the pellets retain much of their translational energy and the post-impact linear velocities are greater than high-friction cases, which leads to much larger post-impact trajectory ranges. The model enables analysts to make more quantitative decisions on the choices of parameters associated with shotgun use and can reduce trial-and-error procedures in testing.

A fundamental numerical model at the powder particle scale based on the material point method (MPM) is developed for selective laser sintering (SLS). In order to describe the thermo-mechanical phenomena, a laser heat source model with a Gaussian energy distribution and the Perzyna viscoplastic model with a return mapping algorithm are employed. The principal process conditions, such as the laser power and radius, and the scanning speed are systematically varied. Based on the obtained temperature distribution generated by laser irradiation under these conditions, elastic–viscoplastic stresses were calculated to evaluate the deformation of powder particle pairs under the driving force of surface tension via a simple two-dimensional test case. The developed MPM model can capture minute changes of the deformation behavior and the temperature distribution history during melting and consolidation at the particle scale. Melting and consolidation of particle pairs during SLS are basic nature in determining the final product quality. The model can help to evaluate variations in the fusion of microscopic areas, melted by a laser, resulting from variations in the process conditions.

The increase in readily available computational power raises the possibility that direct agent-based modeling can play a key role in the analysis of epidemiological population dynamics. Specifically, the objective of this work is to develop a robust agent-based computational framework to investigate the emergent structure of Susceptible-Infected-Removed/Recovered (SIR)-type populations and variants thereof, on a global planetary scale. To accomplish this objective, we develop a planet-wide model based on interaction between discrete entities (agents), where each agent on the surface of the planet is initially uninfected. Infections are then seeded on the planet in localized regions. Contracting an infection depends on the characteristics of each agent-i.e. their susceptibility and contact with the seeded, infected agents. Agent mobility on the planet is dictated by social policies, for example such as "shelter in place", "complete lockdown", etc. The global population is then allowed to evolve according to infected states of agents, over many time periods, leading to an SIR population. The work illustrates the construction of the computational framework and the relatively straightforward application with direct, non-phenomenological, input data. Numerical examples are provided to illustrate the model construction and the results of such an approach.

Phase field modeling of fracture has been in the focus of research for over a decade now. The field has gained attention properly due to its benefiting features for the numerical simulations even for complex crack problems. The framework was so far applied to quasi static and dynamic fracture for brittle as well as for ductile materials with isotropic and also with anisotropic fracture resistance. However, fracture due to cyclic mechanical fatigue, which is a very important phenomenon regarding a safe, durable and also economical design of structures, is considered only recently in terms of phase field modeling. While in first phase field models the material’s fracture toughness becomes degraded to simulate fatigue crack growth, we present an alternative method within this work, where the driving force for the fatigue mechanism increases due to cyclic loading. This new contribution is governed by the evolution of fatigue damage, which can be approximated by a linear law, namely the Miner’s rule, for damage accumulation. The proposed model is able to predict nucleation as well as growth of a fatigue crack. Furthermore, by an assessment of crack growth rates obtained from several numerical simulations by a conventional approach for the description of fatigue crack growth, it is shown that the presented model is able to predict realistic behavior., Deutsche Forschungsgemeinschaft, Projekt DEAL

The pandemic of 2020 has led to a huge interest of modeling and simulation of infectious diseases. One of the central questions is the potential infection zone produced by a cough. In this paper, mathematical models are developed to simulate the progressive time-evolution of the distribution of locations of particles produced by a cough. Analytical and numerical studies are undertaken. The models ascertain the range, distribution and settling time of the particles under the influence of gravity and drag from the surrounding air. Beyond qualitative trends that illustrate that large particles travel far and settle quickly, while small particles do not travel far and settle slowly, the models provide quantitative results for distances travelled and settling times, which are needed for constructing social distancing policies and workplace protocols.

Smoothed particle hydrodynamics (SPH) has become a popular numerical framework of choice for simulating free-surface flows, mainly for Newtonian fluids. The topic regarding the simulation of non-Newtonian free-surface flows, however, remains relatively untouched due to difficulties regarding the computation of viscous forces. In previous approaches, the viscous forces acting on each SPH particle were computed explicitly. Non-Newtonian fluids such as Herschel–Bulkley fluids, the effective viscosity between yielded and unyielded regions can differ by several orders of magnitudes; imposing severe time step restrictions for the simulation for explicit methods. Numerically, this can be seen as a stiff problem. We propose a semi-implicit time-stepping approach where the viscous forces are computed implicitly, within the context of SPH. We demonstrate the convergence of the method via a simple 2D test case.

In this work, a thermal Finite Element model is developed to simulate the performance of a blade-like tool for robotic work cells performing automated garment production using a novel thermoplastic stiffening layer. Uncertainty quantification and sensitivity analysis are applied to determine the most important design properties and optimize key performance metrics for swift and reliable garment assembly. Attention is focused on the geometric and thermal design properties that minimize sensitivity to environmental conditions while maximizing expected productivity. An example design is shown for illustrative purposes. This work may inform future design innovation for similar heating tools and reduce the need for physical experiments and long calibration times on the factory floor.

The goal of this article is to provide basic modeling and simulation techniques for systems of multiple interacting Unmanned Aerial Vehicles, so called “swarms”, for applications in mapping. Also, the paper illustrates the application of basic machine-learning algorithms to optimize their information gathering. Numerical examples are provided to illustrate the concepts.

Electrically induced tissue damage is a coupled phenomenon in multiphysics. Conducting electricity produces heat and this increases the temperature. The soft tissue like skin, organs, brain, or muscles is burnt under successive heating. This damage is modeled by using a damage parameter with a corresponding evolution law above a threshold temperature. Electromagnetism, thermomechanics, and damage modeling creates a set of coupled and nonlinear field equations, by solving them with the aid of the finite element method, we compute a realistic example where the tissue absorbs the electric energy, converts to heat, and gets burnt due to the excessive temperature increase.

The processing of powdered materials by laser processing has become quite widespread. One approach is to deposit a powder bed of material and to “flash” a pattern onto the bed in order to sufficiently heat up the material to sinter and/or fully melt the desired targeted pattern. This avoids rastering a single beam back and forth to produce the pattern. In order to adequately control the thermal fields that are induced by the laser pattern,simulation tools are needed to quickly ascertain the parameter setting needed, such as • powder porosity, • powder conductivity, • beam spatial distribution and • beam temporal duration. The focus of this work is to develop a rapid computational tool that can be used in conjunction with manufacturing systems. The approach is to develop precomputed solutions for point-source “beamlets” and then to create patterns by arranging the point-sources in the proper configuration. The entire thermal field is then created by superposing the solutions. A series of three-dimensional problems are solved to illustrate the approach, which is geared to rapidly solving the response to complex patterns.

In this work, the Smooth Particle Hydrodynamics (SPH) method, a Lagrangian mesh-free numerical scheme , is adapted for the first time to resolve thermal–mechanical–material fields in a range of Laser Fusion Additive Manufacturing processes. The method is capable of simulating large-deformation , free-surface melting, flow, and re-solidification of metallic materials with complex physics and material geometries. A novel SPH formulation for modeling isothermally-incompressible fluids, which allows for the accurate simulation of thermally-driven, liquid-phase metal expansion/contraction, is presented and verified. Fundamental validation of the methodology is performed via comparison with spot laser welding experiments. The methodology is then used to investigate the specific Additive Manufacturing process of the Selective Laser Melting of Metallic, micro-scale particle beds . The physics of a track deposition process is explored through numerical experiments, and the influence of processing parameters on the quality of the finished melt-track is investigated. The unique abilities of using a Lagrangian mesh-free method, as opposed to mesh-based numerical schemes, to model this process are highlighted. The SPH method is found to be a viable and promising numerical tool for simulating laser fusion driven Additive Manufacturing processes.

The goal of this article is to provide an introduction to basic modeling and simulation techniques for multiple interacting unmanned aerial vehicles (UAVs), called swarms, for applications in mapping. The target audience is senior students and young scientists. This review will serve to inform, orient, and direct someone already educated in environmental science but unaware of multiple-UAV interaction models.

The pandemic of 2019 has led to an enormous interest in all aspects of modeling and simulation of infectious diseases. One central issue is the redesign and deployment of ventilation systems to mitigate the transmission of infectious diseases, produced by respiratory emissions such as coughs. This work seeks to develop a combined Digital-Twin and Machine-Learning framework to optimize ventilation systems by building on rapidly computable respiratory emission models developed in Zohdi (Comput Mech 64:1025–1034, 2020). This framework ascertains the placement and flow rates of multiple ventilation units, in order to optimally sequester particles released from respiratory emissions such as coughs, sneezes, etc. Numerical examples are provided to illustrate the framework.

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

This paper focuses on viral decontamination by ultraviolet (UV) irradiation technologies. This work develops an efficient and rapid computational method to simulate a UV pulse in order to ascertain the decontamination efficacy of UV irradiation for a surface. It is based on decomposition of a pulse into a group of rays, which are then tracked as they progress towards the target contact surface. The algorithm computes the absorption at the point of contact and color codes it relative to the incoming irradiation. This allows one to quickly quantify the decontamination efficacy across the topology of a structure., Highlights • The pandemic of 2020 has led to a dramatic increase in research of infectious diseases. • This paper focuses on decontamination by ultraviolet irradiation technologies • Develops an efficient and rapid computational method to simulate a UV pulse to ascertain decontamination efficacy • Based on decomposition of a pulse into a groups of rays, which are then tracked and processed • The algorithm computes the absorption and color codes it relative to the incoming irradiation

Currently available conductive inks present a challenge to achieving electrical performance without compromising mechanical properties, scalability, and processability. Here, we have developed blends of carbon black and the commercially available triblock copolymer (BCP), poly(styrene-ethylene-butylene-styrene)-g-maleic anhydride (SEBS-g-MAH) (FG1924G, Kraton), that can be readily applied as a conductive coating via a spray-coating process, for a wide range of insulating materials (fabric, wood, glass, and plastic). Simple but effective mechanical and chemical modifications of the ingredients can increase the electrical conductivity (∼100 S/m) by an order of magnitude more than previously reported for carbon black composites; moreover, the coatings display excellent mechanical flexibility (tensile strain e ∼ 5.00 mm/mm). To correlate electrical conductivity and nanoscale structural changes with mechanical deformation, small-angle X-ray scattering (SAXS) during in situ tensile testing was performed. We show that the nanocomposite can be produced using low-cost ingredients (∼$ 10/kg), ensuring scalability for fabrication of large-scale devices without specialized material synthesis. Equally important, the phase behavior of block copolymers can enable recovery from physical damage via thermal annealing, which is critical for product longevity.

A technique based on voxel (3D “volume pixels”) representation of microstructures and corresponding digital solution methods is developed for representative volume element type calculations, which avoids computationally expensive steps involved in usual Finite Element procedures such as topologically conforming meshing, mapping, volume integration, stiffness matrix generation and matrix-based solution methods. The process proceeds by converting the material microstructure into voxels. The problem then becomes “digital” on a regular “voxel-grid”, directly manipulating voxel values, allowing extremely fast methods to be used to construct derivatives and the solve the system. In this paper, we illustrate the process of voxelization, derivative construction and solution, and also supply an analysis of the operation counts. Numerical examples are provided to illustrate the approach.

Rapid free-form printing of particle-functionalized materials is an integral component of 3D printing and additive manufacturing. Such processes consist of attaching a dispenser to a robot arm which then releases droplets of specialized mixtures in free-space that are deposited onto a substrate. These approaches are popular because they utilize widely-available, highly-programmable, robots. However, often the release of a complex mixture in free-space is somewhat imprecise, thus electrodynamic field control has been proposed as a possible remedy to enhance the precision of such processes. Specifically, electrodynamic control of the material is achieved by electrifying the released material in the presence of a prescribed ambient electrical field generated from the substrate, in order to guide it to the desired position. There are many components that comprise such a system, thus motivating the construction of a simulation tool framework assembling submodels of the: The modular system structure allows for easy replacement of submodels within the overall framework. Numerical simulations are undertaken to illustrate the overall system model, which is comprised of an assembly of submodels. Afterwards, a Machine Learning Algorithm (MLA) is developed to identify and optimize the proper system parameters which deliver a desired printed pattern. Specifically, an MLA is developed to ascertain the appropriate combination of robotic motion and electrical fields needed to create structures which would be difficult or impossible by purely mechanical means alone. Afterwards, extensions involving more detailed models are then provided, based on the Discrete Element Method.

A mathematical model is developed to characterize the progressive time-evolution of a fragmenting incandescent object. The objective of these models is to provide a spatio-thermal footprint of the fragmentation field, which can be useful to guide fire safety rules in manufacturing workplaces, as well as to estimate fire hazards. Ascertaining the time-evolution of the temperature of the fragments is quite difficult to measure experimentally, which motivates the model development. Initially, analytical models based solely on ballistics, which provide qualitative trends, are developed to provide insight into the fundamental ratios that govern safe operating conditions. Thereafter, rapid numerical spatio-thermal models, which provide quantitative information, are then developed, based on particle methods. The model uses the released energy from the initial blast pulse to provide the starting kinetic energy of the system of particles and then numerically computes the trajectory and thermal state of the fragments under the influence of Numerical examples and provided and extensions to high-fidelity are discussed.

This work presents a review of the formulation for computer simulation based on the discrete element method to analyze granular materials and a validation of the method using different types of tridimensional examples. The individual particulate dynamics under the combined action of particle collisions, particle–surface contact and adhesive interactions is simulated and aggregated to obtain global system behavior. The formulations to compute the forces and momentums developed at the particles are explained in details. The environment and gravity forces are considered as well as the contact forces that occur due the contact between particles and walls, like normal contact forces, frictional contact forces, damping and adhesive bond. The rolling phenomenon is also taken into account and is presented using a standard formulation. A numerical algorithm adapted from Zohdi is also presented. A few tridimensional examples of classical physics are selected to validate the formulations and the numerical program developed and to provide an illustration of the applicability of the numerical integration scheme. For this purpose, each analytical formulation is demonstrated to compare and analyze the numerical results with the analytical one. At the end of this article, a few tridimensional examples of granular materials are simulated. This article contributes to the study of granular materials including the rotation phenomenon using particle methods.

Many applications in additive manufacturing involve the dynamic deposition of powders and the in-flight heating of such material by a laser. In order to characterize such systems, the Discrete Element Method (DEM) is employed. Specifically, this paper focuses on the initial stages of this process by developing a modular discrete-element type multiphysics simulation method for the particle dynamics and heating by a laser and detailed thermal behavior. The objective is to provide researchers with a framework to construct computational tools for this growing industry. In order to achieve this, from a simulation standpoint, the overall particle-mixture system is constructed by coupling submodels for each primary physical process (dynamics and heating) together. An iterative staggering scheme is developed whereby, within every time step, each individual particle is solved “freezing” the state of the remaining multiparticle system. The state of the particle is then updated and the algorithm moves to the next particle in the system and the process is repeated. The overall process sweeps through the entire system repeatedly until convergence is achieved in an appropriate norm. As the system evolves, an error estimate dictates the time-step size that is needed to induce convergence to below an appropriate error level. Thus, the process can be considered as an implicit time-stepping scheme, which is combined with an (internal) iterative staggering process. In order to control rates of convergence within a time-step, the algorithm adjusts the time-step size. If the iterative process does not converge within a desired number of iterations, below an error tolerance, the time-step is reduced. The degree of time-step reduction is determined by utilizing an estimate of the spectral radius of the coupled system. Since the construction of model and solution process is modular, one can easily replace physical submodels with other choices, making it easy to numerically experiment with a variety of models. Qualitative and quantitative analyses are provided, as well as three-dimensional numerical examples. This paper addresses the first of two overall “macrostages” of a complex manufacturing process with DEM. The first stage, addressed in this paper, concentrates on dry-powder materials, which are of a discrete particulate character, using DEM to characterize the deposition and in-flight particle heating. Other papers of the author (Zohdi, 2010, 2013, 2014, 2015 [81,82], 2008) have addressed stage two, namely phase transformations, curing (cooling) and stress analysis, using more appropriate continuum and hybrid DEM-continuum approaches.

Rapid free-form printing of heated polymeric materials, whereby an extruder is attached to a robotic arm, is a growing field. In order to properly plan a complex tool path, one needs to determine the dynamic thermomechanical response of the extruded filament material as the robot arm is moving in free-space. Accordingly, the analysis in this work involves: • Kinematics of the robot arm and the extrusion-printer head, • Dynamics of the extruded polymer filament, • Thermal conduction along the length of the heated filament, • Convective and radiative cooling of the filament through the surroundings and • Curing and solidification of the filament. Numerical simulations are undertaken to illustrate the basic model and a Machine Learning Algorithm is developed to optimize the robotic system to deliver a prespecified structure. Detailed extensions are also discussed.

Production and maker spaces are increasingly generating mixed plastic material waste of varying quality from 3-D printers. Industrial interest is growing in embedding granulated recycled particulate material additives into a virgin binding matrix. Examples include the introduction of granulated mixed recycled materials into 3-D printer material, concrete, and pavement. The stress load-sharing between the particulate additive and the binding matrix is an important factor in design and development of these composite materials. With mixed material additives, a designer is interested in the variation of such predicted load-sharing. However, experimental development is costly and time-consuming, thus analytical and semi-analytical estimates are desired for accelerated development. In this work, we expand on previous analytically correlated phase-averaged micro- and macrostructural loading to include variational effects present in mixed recycled material. In addition, model trade-offs are provided to aid designers in quickly selecting application specific mixtures. This framework identifies the stress contributions, and their variation, to reduce product development time and costs, which could greatly accelerate material recycling and reuse for improved infrastructure materials, low-cost 3-D printer filament, and reduced waste towards a more circular economy.