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A modern circuit board consists of several thousand interacting electronic components. Reduced-order models are often used to rapidly simulate such systems for design purposes, which require the testing of large numbers of design configurations. Reduced-order simulators, such as SPICE, are often used, which are based on a lumped mass nodal analysis. While the intended use of such models is for rigid and isothermal systems, they are also used in order to acquire the temperature evolution in integrated circuits (IC) by computing the dissipation produced in components such as transistors. Generally, reduced-order circuit simulators are not as accurate as a detailed, computationally expensive, direct finite element method (FEM) simulation of an electromagnetic system. In this paper, we determine the inaccuracies introduced in a reduced-order model by simulating the same system by means of a detailed three-dimensional, coupled, and nonlinear FEM analysis for electromagneto-thermomechanical fields. Specifically, we compare results from a one-dimensional SPICE simulation to the three-dimensional transient FEM computation. Using SPICE, we calculate the electric potential with the known resistance providing Joule heating of a resistor on an IC. In an FEM computation, we solve coupled governing equations for electromagnetic potentials, determine electric current distribution, and integrate over the continuum body in order to calculate the dissipated power. We find out that there is an up to 30% of discrepancy between computations from SPICE and FEM in terms of the dissipation. After an intensive study explained in this manuscript, we obtain the root cause of the aforementioned significant difference between SPICE and FEM. The geometrical simplification from three-dimensional continuum to a one-dimensional model brings in an inadequate assumption on the boundary conditions. This assumption generates a significant error in the determined power from SPICE in the case of a resistor, concretely a standard micro-metal electrode leadless face (MELF) studied herein.

We demonstrate thin-film repulsive-force electrostatic actuators that employ a new electrode pattern and are useful for low-force actuation applications. Compared to prior patterns, the new electrode geometry increases electrostatic force production by an order of magnitude (at equal voltages) and eliminates the most common shorting failure modes. These electrostatic actuators have stable open-loop operation with no pull-in instability, low mechanical hysteresis, and peak force in rest configurations. The actuators are fabricated with a planar, flex-circuit manufacturing process, allowing production at scale and over large areas. Two-layer out-of-plane linear actuators (25 × 10 mm electrode area) were characterized: with 0–1000 V inputs (40 × 106 V/m), blocked normal forces of 9.03 mN (36.1 Pa) were generated, and controllable linear displacements up to 511 μm were measured across an open loop bandwidth of 43 Hz. Finally, we present a 290 mg 1-DoF micro-mirror system for laser beam steering that employs a two-layer out-of-plane rotational actuator for open-loop stable operation with controlled angular displacements up to 5.1° at 1000 V/16 Hz.

As 3D printing has matured, the use of more complex materials has increased. In particular, particle-functionalized inks are now relatively wide-spread. Because of the desire to have faster throughput for industrial-scale printing, electrically-driven flow of such materials is being pursued. In many cases, such fluids consist of an electrically-neutral base solvent with embedded charged particles. As one increases the volume fraction of particles, two effects effects arise: (1) an increase in effective overall viscosity fluid and (2) an increase in the induced electrical force that can be applied. In the present analysis, the governing equations for the required pressure gradient in a pipe to move the fluid with a constant flow rate are derived. A key nondimensional scaling ratio governing the relative contribution of electrical and viscous fluid forces to the system behavior is also identified. Numerical examples are provided to illustrate the results.

Unmanned Aerial Vehicles (UAVs), in particular quadcopters, have become extremely prevalent, driven by their low cost and ease of control. Unfortunately, privacy concerns related to the ubiquity of UAVs have prompted substantial citizen interest in the shooting down of UAVs that trespass onto their property, although the legality thereof is unclear. In this work, the dynamical response of a quadcopter to a series of randomly external impulses, which could be generated by objects launched toward the UAV, such shotgun pellets, etc., is formulated. A Discrete Element Method (DEM) is developed to describe the breakup of the quadcopter, in conjunction with a staggered implicit time-stepping scheme. The use of DEM allows for fragmentation of the quadcopter and also to compute the trajectories and distribution of the resulting debris field.

There are many emerging manufacturing processes whereby surface structures are processed by spatially laser patterning of an entire feature at a time, as opposed to rastering a small beam. It is important to ascertain and ideally control the induced thermal fields underneath the pattern. This paper develops a computational framework to rapidly evaluate the induced thermal fields due to application of a laser on the surface. The aggregate thermal fields are efficiently computed by superposing individual “beamlet” heat-kernel solutions, based on Green’s functions, to form complex surface patterns. The utility of the approach is that laser-process designers can efficiently compute the results of selecting various system parameters, such as spatially-variable laser intensity within a pattern. This allows one to rapidly compute system parameter studies needed in the manufacturing of new products. Included are: Three-dimensional examples are provided to illustrate the technique. The utility of the approach is that an analyst can efficiently ascertain a large number of laser-input scenarios without resorting to computationally-intensive numerical procedures, such the Finite Element Method.

Electrical high voltage (HV) machines are prone to corona discharges leading to power losses as well as damage of the insulating layer. Many different techniques are applied as corona protection and computational methods aid to select the best design. In this paper we develop a reduced-order model in 1D estimating electric field and temperature distribution of a conductor wrapped with different layers, as usual for HV-machines. Many assumptions and simplifications are undertaken for this 1D model, therefore, we compare its results to a direct numerical simulation in 3D quantitatively. Both models are transient and nonlinear, giving a possibility to quickly estimate in 1D or fully compute in 3D by a computational cost. Such tools enable understanding, evaluation, and optimization of corona shielding systems for multilayered coils.

A hybrid Lagrangian Voronoi–SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

The trajectories and branching of electrical discharges through gaseous atmospheres, such as lightning and coronal emissions from high-voltage electromachinery, are of interest in a variety of applications. Multiple branches can evolve in an initially poor atmospheric conductor when a strong electrical discharge builds up, then propagates through the atmosphere by dielectric breakdown. Multiple branches can be generated in gases because of the disordered character of the media at the microscale, with an overall influence occurring from the ambient electric fields. In this paper, we develop a sufficiently flexible computational model to describe discharge trajectory and branching. The framework allows analysts to rapidly simulate thousands of electrical discharge scenarios, in order to statistically explore the dependency of the overall system behavior on the relevant physical parameters.

The increase in readily available computational power raises the possibility that robust agent-based modeling can play a productive role in the analysis of population dynamics. Accordingly, the objective of this work is to develop a robust agent-based computational framework to investigate the emergent structure of initially intermeshed hostile, competing, populations on a global scale. Specifically, we develop a model based on discrete entities (agents), each with their own interaction rules with their immediate neighbors, innate skill sets, reproductive rates, mobility and lifespans to represent a population. The global population is then allowed to evolve according to these local rules over many generations. The biological systems-level applications are numerous, stemming from human conflict on the macroscale to microbes on the microscale. Numerical examples are provided to illustrate the model construction and the results of such an approach.

In many structural applications, there is growing industrial interest in using new microscale particle-enhanced composite materials. During the design development of such machinery and materials it is advantageous to ascertain the stress load-sharing between the added particles and the binding matrix, in order to make estimates of the device’s useful life and the material performance. Accordingly, in this work, we correlate the phase-averaged microstructural stress levels caried by the particles and matrix to the macrostructural loading. Model problems are studied whereby macroscale stresses are determined using a structural-scale model and the microscale stresses are then computed by constructing stress concentration functions. This provides analysts with a novel and easy to use design framework that clearly identifies the stress contributions from the microscale and the macroscale, in order to reduce product development time and costs. Examples are provided to illustrate the approach.

A widespread use of lasers in additive manufacturing is to induce a given temperature and a phase transformation in materials deposited onto a substrate. For a laser to induce a phase transformation in the material, the power intensity must be sufficiently high to induce melting and, in all cases, stay below a vaporization or burn-off temperature of the target material. Oftentimes, there is variability in the laser input to the target zone. For a process designer, a central question is to determine the uncertainty of the resulting target state, i.e., temperature and state (solid or melted), due to uncertainty in the energy (laser) input. This motivates the present work, which integrates relatively fundamental heat transfer models that describe the thermal effects due to (a) laser irradiation, (b) heat conduction into the surface of deposition, (c) infrared radiation outwards into the surroundings, (d) convection due to an exhaust apparatus to control the cooling of the system, and (e) phase transformations, for a dry Nylon 6 powder as a sample material. One key advantage of this framework is that it is amenable to a sensitivity and uncertainty analysis with respect to any of its parameter inputs. Accordingly, uncertainty quantification studies are also undertaken to ascertain the relationship between variation in laser input to variation in the processed material state. Examples will be presented to illustrate the thermal behavior of the numerical model. Due to its simplicity, this framework is designed to be computationally implemented in a straightforward fashion. The model allows for rapid computation and sensitivity analyses, which are provided as numerical examples. Extensions are also given to include mass transport (losses) due to ablation of the target material.

Within the scope of additive manufacturing (AM) methods, a large number of popular fabrication techniques involve high-temperature droplets being targeted to a substrate for deposition. In such methods, an “ink” to be deposited is tailor-made to fit the desired application. Concentrated stresses are induced on the substrate in such procedures. A numerical simulation framework that can return quantitative and qualitative insights regarding the mechanical response of the substrate is proposed in this paper. A combined smoothed particle hydrodynamics (SPH)-finite element (FE) model is developed to solve the governing coupled thermo-mechanical equations, for the case of Newtonian inks. We also highlight the usage of consistent SPH formulations in order to recover first-order accuracy for the gradient and Laplacian operators. This allows one to solve the heat-equation more accurately in the presence of free-surfaces. The proposed framework is then utilized to simulate a hot droplet impacting a flat substrate.

Selective Laser Melting (SLM) is an emerging Additive Manufacturing technology for metals. Complex three dimensional parts can be generated from a powder bed by locally melting the desired portions layer by layer. The necessary heat is provided by a laser. The laser–matter interaction is a crucial physical phenomenon in the SLM process. Various modeling approaches with different degrees of complexity exist in the literature to represent the laser–matter interaction within a numerical framework. Often, the laser energy is simply distributed into a specified volume. A more precise approach is ray tracing. The laser beam can be divided into moving discrete energy portions (rays) that are traced in space and time. In order to compute the reflection and absorption usually a triangulation of the free surface is conducted. Within meshfree methods, this is a very expensive operation. In this work, a computationally efficient algorithm is developed which avoids triangulation and can easily be combined with meshfree methods. Here, the suggested ray tracing algorithm is exemplary coupled with the stabilized Optimal Transportation Meshfree Method. The importance of ray tracing is evaluated by simulating the fusion of metal powder particles. A comparison of the results with a volumetric heat source approach shows that ray tracing significantly improves the accuracy of absorption and vaporization.

This work investigates the effects of a pressure increase in deformable fluid-filled biochannels, such as arteries and veins. Simple qualitative expressions are developed relating pressure-induced changes to the biochannel expansion, volumetric flow rate, and biochannel wall stress. Such relations are necessary for a rapid analysis in potential applications such as post-traumatic stress, hemorrhagic strokes, atherosclerotic plaque buildup, etc. The relations are based on the development of functions that correct classical pressurized thin-tube expressions for hoop stress for finite deformations.

The objective of this work is to model and simulate aerial drops of fire retardants in dangerous fire environments. Specifically, the work develops a computational framework for a model problem combining: • [1.] A meshless discrete element component that tracks the trajectory of released airborne materials from a controlled aircraft, ranging from retardant powders to encapsulated packets, subjected to prevailing wind velocities and fire-driven updrafts. • [2.] A Machine Learning Algorithm (MLA) to rapidly ascertain the optimal aircraft (unmanned or manned) dynamics to maximize the fire-retardant release effectiveness (released material usage and target impact). The framework is designed to enable Digital Twin type technologies, i.e. digital replicas that run in real time with the physical system. However, it is also designed to run at much faster rates, in order to enable MLA’s to optimize the planning, by running quickly on laptops and mobile systems. The overall guiding motivation is to provide a useful tool to enable rapid flight-path planning for aerial first-responders in real-time and to train pilots. Numerical examples are provided to illustrate the process.

Across many modern industries, as technologies have matured, the use of more complex processes involving multiphase materials has increased. In the food industry, multiphase fluids are now relatively wide-spread, in particular, because of the desire to have faster throughput for large-scale food production. In many cases involving transport, such materials consist of a fluidized binder material with embedded particles. As one increases the volume fraction of particles, a corresponding increase in effective overall viscosity occurs. Often, during the process, the material must be heated, for example, to ensure food safety, induce pasteurization, sterilization, etc. For real-time control, this requires rapidly computable models to guide thermal processing, for example by applied electrical induction. In the present analysis, models are developed for the required heating field (electrically induced) and pressure gradient needed in a pipe to heat a multiphase material to a target temperature and to transport the material with a prescribed flow rate.

In this work, a semi-analytical approach presenting a laminar particle-laden flow in curved lumen with permeable walls is developed. In order to illustrate its practical use, the fluid dynamics modeling of a human Juxtamedullary nephron is presented. Close agreement between the calculated values and the medical literature is found. The presented modeling approach provides an essential guide for researchers and designers to rapidly model and analyze the behavior of laminar particle-laden flows in lumen with permeable walls.

In this paper, we investigate the explosion of a set of charged particles in an electromagnetic field and the progressive time-evolution of the blast envelope. It is shown that the initial spherical blast envelope evolves into the shape of an ellipsoid whose longitudinal axis is aligned with the magnetic field. Specifically, the individual particles rotate around the longitudinal axis, and rotate in decaying orbits until they become stationary, leaving a stationary overall ellipsoidal configuration of particles. In order to investigate this system, a direct multiparticle model is constructed, which balances the detonation energy released from the initial blast pulse with the subsequent particle-system kinetic energy and then computes the trajectories of the discrete interacting material under the influence of the electromagnetic field and drag from any surrounding medium. Under certain simplifying assumptions, the model can be solved for analytically, which provides a guide to identifying the key parameters that control the evolving blast envelope. Three dimensional examples are provided to illustrate the framework/method.

Author(s): Queiruga, A; Zohdi, T | Abstract: A computational framework for assisting in the development of novel textiles is presented. Electronic textiles are key in the rapidly growing field of wearable electronics for both consumer and military uses. There are two main challenges to the modeling of electronic textiles: the discretization of the textile microstructure and the interaction between electromagnetic and mechanical fields. A director-based beam formulation with an assumed electrical current is used to discretize the fabric at the level of individual fibrils. The open-source package FEniCS was used to implement the finite element model. Contact integrals were added into the FEniCS framework so that multiphysics contact laws can be incorporated in the same framework, leveraging the code generation and automated differentiation capabilities of FEniCS to produce the tangents needed by the implicit solution method. The computational model is used to construct and determine the mechanical, thermal, and electrical properties of a representative volume elements of a plain woven textile. Dynamic relaxation to solve the mechanical fields and the electrical and thermal fields is solved statically for a given mechanical state. The simulated electrical responses are fit to a simplified Kirchhoff network model to determine effective resistances of the textile. Copyright © 2016 John Wiley a Sons, Ltd.

This paper analyzes the sensitivity of high-frequency radiation scattering in particulate media, to particle surface roughness. Ray-tracing theory and computation are employed. Since the magnitude of the Poynting vector ray, the irradiance, is the appropriate quantity to be tracked, the behavior of the reflectance, which controls the ratio of the reflected and incident Poynting vector magnitudes, is of primary concern. The reflectance is a highly nonlinear function of the refractive indices and angle of incidence. The present work first addresses the relationship between a single scatterer’s sensitivity to its surface roughness and then the response of a large number of scatterers to the surface roughness. The analysis indicates that, for a single scatterer, the sensitivity of the response to roughness decreases, up to a point, and then increases again, i.e., it is nonmonotone. However, for a system of multiple scatterers, this effect vanishes, due to multiple internal reflections which dominate the overall response characteristics. While it was relatively straightforward to compute the overall sensitivity of a single scattering body, for example a sphere, when multiple reflecting bodies are considered, numerical simulations are necessary because the reflected rays from one “rough” body will, in turn, be reflected to another “rough” body, etc. Examples are given for a system of randomly distributed scatterers.

Most modern electromagnetic devices consist of dielectric and magnetic particulate composites. Predicting the effective electric permittivity and effective magnetic permeability of the envisioned composite is of great importance in validating the design for such applications. In this work, we propose a numerical method based on Yee's scheme and statistically generated representative volume element to estimate these effective electromagnetic properties for linear isotropic composites made with ellipsoidal particles. By considering particle geometry and composite microstructure precisely, it provides a more accurate tool for their design than available analytical bounds. Several numerical examples of composite microstructures are presented to demonstrate the capability of the proposed method. Comparison with analytical bounds and experimental results from literature is conducted to show validity. Keywords: Electrical properties, Magnetic properties, Computational modeling, Composites design

There are many emerging manufacturing processes whereby structures are formed by depositing materials onto substrates in order to build up layers or coatings. The processes are often referred to as “additive manufacturing”. Particle-based additive manufacturing processes utilize deposition of streams of particles to build layers upon substrate surfaces. Oftentimes, the substrates are fragile/sensitive, and could become damaged if the induced stresses due to deposition are too high. In these cases, knowledge of the substrate stresses is important. This paper develops a computational-mechanics framework to rapidly evaluate the induced substrate stresses due to multiple, simultaneous, surface particle contact events. The aggregate substrate stresses are efficiently computed by superposing individual particle contact solutions, based on classical Boussinesq solutions, coupled to a multibody dynamics formulation for the interacting particles. The utility of the approach is that process designers can efficiently compute the results of selecting various system parameters, such as deposition speed, particle-stream configuration, etc. This allows one to rapidly compute system parameter studies needed in new product development. Three-dimensional examples are provided to illustrate the technique.

In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.

Since binder-less polycrystalline diamond (BLPCD) has no macro cleavage planes and highest hardness, it is desirable material for micro milling tools. However, fabricating micro tools made of BLPCD by conventional method such as grinding is very time consuming due to its extremely high hardness. This paper describes the successful results obtained in our recent study on productive machining of BLPCD using femtosecond-pulsed laser (FSPL). The ablation effect of BLPCD by FSPL has been studied by conducting a series of experiments. Also, the predictability of ablation effect of FSPL when machining BLPCD has been evaluated by introducing numerical analysis model.

The objective of this paper is to focus on one of the “building blocks” of additive manufacturing technologies, namely selective laser-processing of particle-functionalized materials. Following a series of work in Zohdi (Int J Numer Methods Eng 53:1511–1532, 2002; Philos Trans R Soc Math Phys Eng Sci 361(1806):1021–1043, 2003; Comput Methods Appl Mech Eng 193(6–8):679–699, 2004; Comput Methods Appl Mech Eng 196:3927–3950, 2007; Int J Numer Methods Eng 76:1250–1279, 2008; Comput Methods Appl Mech Eng 199:79–101, 2010; Arch Comput Methods Eng 1–17. doi: 10.1007/s11831-013-9092-6 , 2013; Comput Mech Eng Sci 98(3):261–277, 2014; Comput Mech 54:171–191, 2014; J Manuf Sci Eng ASME doi: 10.1115/1.4029327 , 2015; CIRP J Manuf Sci Technol 10:77–83, 2015; Comput Mech 56:613–630, 2015; Introduction to computational micromechanics. Springer, Berlin, 2008; Introduction to the modeling and simulation of particulate flows. SIAM (Society for Industrial and Applied Mathematics), Philadelphia, 2007; Electromagnetic properties of multiphase dielectrics: a primer on modeling, theory and computation. Springer, Berlin, 2012), a laser-penetration model, in conjunction with a Finite Difference Time Domain Method using an immersed microstructure method, is developed. Because optical, thermal and mechanical multifield coupling is present, a recursive, staggered, temporally-adaptive scheme is developed to resolve the internal microstructural fields. The time step adaptation allows the numerical scheme to iteratively resolve the changing physical fields by refining the time-steps during phases of the process when the system is undergoing large changes on a relatively small time-scale and can also enlarge the time-steps when the processes are relatively slow. The spatial discretization grids are uniform and dense enough to capture fine-scale changes in the fields. The microstructure is embedded into the spatial discretization and the regular grid allows one to generate a matrix-free iterative formulation which is amenable to rapid computation, with minimal memory requirements, making it ideal for laptop computation. Numerical examples are provided to illustrate the modeling and simulation approach, which by design, is straightforward to computationally implement, in order to be easily utilized by researchers in the field. More advanced conduction models, based on thermal-relaxation, which are a key feature of fast-pulsing laser technologies, are also discussed.

In the original publication of the article, the sentence “If we assume that everyone in the beginning is susceptible (S(t = 0) = 1).

The objective of this work is to illustrate how to algorithmically integrate Machine-Learning Algorithms (MLA’s) with multistage/multicomponent fire spread models. In order to tangibly illustrate this process, this work develops a framework for a specific model problem combining: (I) a meshless discrete element “submodel” that tracks the trajectory of airborne hot particles/embers, subject to prevailing wind velocities and updrafts, (II) a topographical “submodel” of the ambient combustible material whereby airborne embers that make contact are allowed to start secondary fires (if conditions are appropriate), combined with ground-based surface spread and burn rates for generating new embers, new updrafts (due to hot air), etc., and (III) a Machine-Learning Algorithm to rapidly ascertain the multi-submodel system parameters that force the overall model to match observations. The submodels compute both ground and airborne hot-ember driven fire propagation, as well as subsequent distribution of debris/soot, which is important for air-quality assessment. The overall framework is designed for use in digital twin technology, which refers to an adaptive digital replica of a physical system, whereby model updates are continuously in near real-time. This necessitates a rapid simulation paradigm that can easily interface with telecommunications, cameras and sensors. The presented framework is designed to run quickly on laptops and hand held devices, with the guiding principle being to make it potentially useful for first-responders in real-time.

Lidar and other time-of-flight technologies have recently received significant attention in both academic and industrial biomechanics communities, driven by technological advances in human body scanners . This paper develops an efficient and rapid computational method to simulate fast flash-type single-pulse Lidar, based on decomposition of a Lidar pulse into a group of rays, which are then tracked and processed. This allows one to quickly quantify the uncertainty in the response by identifying regions where the return signal will be erroneous due to multiple reflections.

In most problems of mathematical physics the true solutions are nonsmooth, i.e., they are not continuously differentiable. Thus, we cannot immediately apply a Galerkin approach. For example, in the equation of static mechanical equilibrium

There are two main approaches to solving systems of equations resulting from numerical discretization of solid mechanics problems, direct and iterative.

As we have seen in the one-dimensional analysis, the essential idea in the finite element method is to select a finite dimensional subspatial approximation of the true solution and form the following weak boundary problem

The finite element method is a huge field of study. This set of notes was designed to give students only a brief introduction to the fundamentals of the method.

Albeit a bit repetitive, we follow similar constructions to those used in the one-dimensional analysis of the preceding chapters. This allows readers a chance to contrast and compare the differences between one-dimensional and three-dimensional formulations.

A key part of emerging advanced additive manufacturing methods is the deposition of specialized particulate mixtures of materials on substrates. For example, in many cases these materials are polydisperse powder mixtures whereby one set of particles is chosen with the objective to electrically, thermally, or mechanically functionalize the overall mixture material and another set of finer-scale particles serves as an interstitial filler/binder. Often, achieving controllable, precise deposition is difficult or impossible using mechanical means alone.

In numerous industries, particle-laden fluids are a key part of the fabrication of products such as (1) casted machine parts, (2) additively manufactured and 3D printed electronics and medical devices, and even (3) slurry processed food to name a few.

In certain applications, because the substrate is fragile, knowledge of the induced stresses is important in order to control the process.

Throughout this work, boldface symbols denote vectors or tensors. Furthermore, we exclusively employ a Cartesian basis.

The previous analytical expressions provide good way to estimate and optimize material combination for effective properties, while controlling local field fluctuations. However, in order to probe the response of a given material combination more deeply, in particular the time-dependent behavior when it is thermoformed, one must resort to numerical methods.

During the development of new particulate-functionalized materials, experiments to determine the appropriate combinations of particulate and matrix phases are time-consuming and expensive.

This chapter develops a computational model and corresponding solution algorithm for the rapid simulation of the laser processing and targeted localized heating of materials composed of discrete particles that are packed together, which goes beyond a simple Beer–Lambert representation. Such materials possess a complex microstructure which contains gaps and interfaces.

The typical use of the bounds from the previous chapter is to make an estimate of the effective properties by forming a convex combination of them in the following manner.

Dry powders require different modeling and simulation tools to characterize their behavior. One family of methods that is ideally suited to this task are discrete element methods. This chapter introduces the reader to this type of modeling.

The adoption of micromechanical material models and computational methods in additive manufacturing and 3D printing has the potential to bring a level of systematic analysis that can make it a reliable large-scale manufacturing process.