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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.

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 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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

Obscurants are often clouds of dispersed particulate materials whose purpose is to mask a given object. The objective of this paper is to develop a simple discrete-ray/discrete-particle model in order to enable rapid assessment of the response of an obscurant cloud to an incoming high-frequency beam. The beam is decomposed into a set of discrete rays and the obscurant is represented by a discrete set of scattering particles. Ray-tracking is used to calculate the transient propagation of the rays and the absorption of energy by the particles. Examples are given, comprised of concentrated incident beams, their propagation into the obscurant cloud, and the subsequent reflection and transmitted aggregate response. Basic system trends are computed, varying the randomly dispersed particle shapes from spherical to oblate objects, which correlate the total amount of volume and surface area material available to interact with the beam and the overall scattering response. This allows further correlation of the obscurant cloud performance to the weight of the material, which is important for portable containers of dispersible obscurants, such as smoke grenades. Specifically, the model allows for rapid quantification of the modest reduction of scattering efficiency of flakes, relative to spheres, but which have significantly less weight than spheres. Thus, there is a trade-off between the weight of the dispersed system and its scattering efficiency.

The general problem of a loosely flowing erosive granular jet undergoing impact with a compliant surface is common in many manufacturing processes, and also in the operating environment of a variety of machine parts. This paper presents a three-dimensional, collision-driven discrete particle simulation framework for investigating the dynamics of a jet of erosive particles impacting a surface with a specified porosity and compliance. The framework is capable of handling repeated collisions between incoming particles and rebounding particles, and between particles and surfaces. It is also capable of performing a coupled simultaneous calculation of sub-surface stresses in the material, assuming a certain porosity. Well illustrated numerical examples are presented with detailed analysis for investigations on the mechanics and energetics of the interfering collisions in eroding jets close to the target surface, on the effect of such interference on the material erosion, and on the evolving stress levels and potential damage zones under the action of impact. Particularly, the assumption of considering first-order collisions between oncoming and rebounding jet particles is re-examined. The influence of repeated collisions on energy transferred to the surface was found to be significant under conditions which involves high particle numbers or fluxes, and also high degrees of inelasticity. The overall trends for parametric variations were found to be in accordance with reported trends in the literature.

An important phenomenon in the field of thermoelectric conversion in certain materials is the Seebeck effect, which is characterized by an electrical field, E being produced by a temperature gradient, E = S ∇ θ , where S is known as the (isotropic) Seebeck number. The objective of this note is to develop bounds on the effective thermoelectric Seebeck property for heterogeneous mixtures of materials. Specifically, we develop bounds on 〈 E 〉 Ω = S ∗ 〈 ∇ θ 〉 Ω , where S ∗ is the effective Seebeck number for the mixture, where the averaging operator is defined as 〈 · 〉 Ω = def 1 | Ω | ∫ Ω ( · ) d Ω over a statistically representative volume element with domain Ω , using only the pointwise cross-correlation properties of the material and the average thermal fields. .

As a method for bonding powdered materials, sintering has distinct advantages, such as the production of a near final-shape of the desired product, without the need for significant post-processing. However, sintering has certain deficiencies, such as incomplete or weak bonding. Research is ongoing to improve the process. One approach to improve sintering processes of powdered materials is via electrically enhanced bonding, whereby electricity is pumped through the material, while it is compressed in a press, in order to induce Joule-heating. This paper develops a computationally based model for the direct simulation of electrically enhanced sintering of powdered materials using particle-based methods. The overall approach is to construct three coupled sub-models which primarily involve: (a) particle-to-particle mechanical contact, (b) particle-to-particle thermal exchange and (c) particle-to-particle electrical current flow. These physical processes are strongly coupled, since the dynamics dictates which particles are in contact and the contacts determine the electrical flow. The flow of electricity controls the Joule-heating and the induced thermal fields, which soften the material, leading to enhanced particle binding. The strong multiphysics-coupled sub-models are solved iteratively within each time-step using a recursive staggering scheme, which employs temporal adaptivity to control the error. If the process does not converge (to within an error tolerance) within a preset number of iterations, the time-step is adapted (reduced) by utilizing an estimate of the spectral radius of the coupled system. The modular approach allows for easy replacement of submodels, if needed. Numerical examples are provided to illustrate the model and numerical solution scheme.

This work is concerned with the identification of microscale properties of additives for base lubricants in order to reduce heat generation. An application of specific interest is the thin film lubrication of bearings. In order to isolate the thermal effects in the fluid film, we assume that the bearing and housing are insulated. A relation for the temperature rise in the fluid film between the bearing and housing is developed as a function of the rotation speed, the viscosity of the base lubricant and properties of the additives, namely (1) their viscosities, (2) their mass density, (3) their heat capacity and (4) volume fraction, which are free design parameters. Nondimensionalization of the developed relations allows for the construction of a design parameter space which can identify desirable parameter combinations that deliver a target value of heat generation reduction and simultaneously deliver the appropriate overall viscosity of the modified lubricant mixture.

Printed electronics are becoming widespread in modern industrial devices. In many of the manufacturing processes of printed electronics, one step is the deposition of initially molten (or liquid), microscale, “print-lines” of material onto a flexible substrate. As the deposited molten print-line solidifies, the bonded print-line and substrate may have the tendency to curl (attain a finite curvature), due to the differences in the thermal expansion coefficients, elastic properties, etc. The quality and durability of the solidified print-line (which is mechanically-weak) is adversely affected by residual tensile stress states. Tensile stress states have a tendency to induce damage in the form of cavities or cracks in the deposited material, which would hinder the printed electronics operation. Therefore, ideally, one would like the solidified print-line to be in a state of compression. Inducing a compressive stress-state in the print-line is particularly important in the vicinity of the substrate interface, since damage in that location may also initiate delamination of the deposited material and, eventually, a malfunction of the intended printed electronics application. In this work, employing an elementary thermo-mechanical model, a mathematical expression is derived for the combination of system parameters needed to ensure that the print-line material at remains in a compressive state at the bimaterial interface.

This work develops a rigorous variational upper bound for the difference between thermal fields generated in uniform media and thermal fields generated in heterogeneous media, for the same external loading. The bound can be calculated in a simple manner, with knowledge only of the heterogeneous material properties and a relatively easy-to-compute thermal field associated with a uniform medium. In order to evaluate the bound, the difficult-to-compute thermal field, associated with the heterogeneous material, does not need to be calculated. Three-dimensional numerical examples are provided to illustrate the results.

© 2016 Elsevier B.V. An electromagnetic beam model is developed for the simulation of actuated electronic textiles. The beam is solved using a nonlinear director-based kinematic description with additional temperature and electric potential fields along its length. The three fields are fully coupled by mutual dependences on the deformation, Lorenz force, back electromotive force, temperature dependent constitutive responses, and the Seebeck effect. Instead of solving Maxwell's equations in full detail, a quasistatic approximation is used to solve the electric potential in the presence of a moving material medium. The current-carrying beam approximation is used to further simplify the solution space for the potential. While this formulation alleviates the spatial and temporal discretization restrictions, the coupled problem is an index-1 semi-explicit Differential Algebraic Equation requiring special treatment. The time dependent problem is solved using different Runge-Kutta methods. Diagonally implicit Runge-Kutta methods and explicit Runge-Kutta methods using implicit solution of the electric potential problem are explored. The finite element model is implemented using the open source package FEniCS, which is able to automatically generate the linearizations of the multiphysics equations required for the implicit solutions. A model problem is constructed with which to test and analyze the physical formulation and numerical solution techniques. The time stepping methods are verified using the convergence orders of the higher-order Runge-Kutta methods. Runtime comparisons show that the explicit methods are generally more computationally efficient than the implicit schemes used for this problem. For the implicit schemes, a staggered solution is significantly faster than a monolithic solution at most time step sizes. However, at very large time steps, such as those that would be used for dynamic relaxation, the monolithic solution can be more efficient than the staggered solution.

Selective laser sintering (SLS) is an additive manufacturing technology whereby one can 3D print parts out of a powdered material. However, in order to produce defect free parts of sufficient strength, the process parameters (laser power, scan speed, powder layer thickness, etc.) must be carefully optimized depending on material, part geometry, and desired final part characteristics. Computational methods are very useful in the quick optimization of such parameters without the need to run numerous costly experiments. Most published models of this process involve continuum-based techniques, which require the homogenization of the powder bed and thus do not capture the stochastic nature of this process. Thus, the aim of this research is to produce a reduced order computational model of the SLS process which combines the essential physics with fast computation times. In this work the authors propose a coupled discrete element-finite difference model of this process. The powder particles are modeled as discrete, thermally and mechanically interacting spheres. The solid, underneath substrate is modeled via the finite difference method. The model is validated against experimental results in the literature and three-dimensional simulations are presented.

This work investigates the deformation of electrified textiles in the presence of an externally supplied magnetic field ( B ext ). The electrification is delivered by running current ( J ) through the fibers from an external power source. Of primary interest is to ascertain the resulting electromagnetic forces imposed on the fabric, and the subsequent deformation, due to the terms J × B ext and P E , where P is the charge density, E is the electric field and the current given by J = σ ( E + v × B ext ) , where σ is the fabric conductivity, and v is the fabric velocity. As the fabric deforms, the current changes direction and magnitude, due to the fact that it flows through the fabric. The charge density is dictated by Gauss’ law, ∇ · D = P , where D = ϵ E , ϵ is the electrical permittivity and D is the electric field flux. In order to simulate such a system, one must solve a set of coupled equations governing the charge distribution, current flow and system dynamics. The deformation of the fabric, as well as the charge distribution and current flow, are dictated by solving the coupled system of differential equations for the motion of lumped masses, which are coupled through the fiber-segments under the action of electromagnetically-induced forces acting on a reduced order network model. In the work, reduced order models are developed for (a) Gauss’ law ( ∇ · D = P ), (b) the conservation of current/charge, ∇ · J + ∂ P ∂ t = 0 , and (c) the system dynamics, ∇ · T + f = ρ d v dt , where T is the Cauchy stress and f represents the induced body forces, which are proportional to P E + J × B ext . A temporally-adaptive, recursive, staggering scheme is developed to solve this strongly coupled system of equations. We also consider the effects of progressive fiber damage/rupture during the deformation process, which leads to changes (reduction) in the electrical conductivity and permittivity throughout the network. Numerical examples are given, as well as extensions to thermal effects, which are induced by the current-induced Joule-heating.

For composite materials, two quantities that are useful for characterizing the contribution of inhomogeneities in a matrix material to the overall properties are (1) the individual H-tensor, Hi, which describes the contribution of a single inhomogeneity and (2) the overall strain concentration tensor, which describes the relationship between the overall volumetric strain to the average strain of all of the inhomogeneities. In this paper, we develop a relationship expressing the overall H-tensor, \({\mathcal{H}}\) , in terms of the overall strain concentration tensor. An important feature of the derivation is that it allows for rigorous upper and lower bounds on the overall H-tensor. In the special case that the inhomogeneities are all the same, with the same orientation, then \({\mathcal{H} = {\bf H}_i}\) , and the results derived for \({\mathcal{H}}\) also hold for Hi.

The microstructure of chain-mail (CM) armor consists of a network of small links that are connected together to form a sheet. A network-type model, amenable to straightforward numerical simulation, is formulated, where the links are modeled as supporting only axial (tensile) loading, and where the interconnections are idealized as three-dimensional frictionless pin-joints. Because of its use as a ballistic shield, the strain-rate dependent thermo-mechanical (viscoplastic) response is important, due to thermal softening. The philosophy behind the proposed direct modeling approach is to harness the dramatic increases in readily available scientific computing to simulate realistic responses of structural CM, by starting directly at the microscale, where relatively simple description of the material is possible. By employing enough of these simple structural elements, one can build an entire macroscale sheet of CM. The deformation of the CM is dictated by solving a (“link-coupled”) system of differential equations for the motion of the interconnected masses. Large-scale simulations, illustrating the thermomechanical response of chain-mail material armor, undergoing impact with a rigid indenter, are presented to illustrate the potential of the approach in delivering realistic responses, involving dynamic rupture and penetration of structural CM.

Doping dielectric materials with particulates for use in electronic device applications is wide-spread, particularly for energy-storage devices such as ultracapacitors and batteries. This work investigates the resulting distortion of the electrical fields in multiphase (particle and matrix) material systems. Of particular interest is to ascertain safe overall electrical loading conditions in order to avoid current overload in heterogeneous media. Specifically, it is important to determine the phase-wise Joule-type heating field, formed by the inner product of the current and electric fields. General estimates are developed, and two asymptotic cases are studied: (1) high-conductivity (“superconducting”) particles added to a lower relative-conductivity matrix and (2) low-conductivity (“insulator”) particles added to a higher relative-conductivity matrix. The expressions developed provide a relatively easy guide for the selection of dopants in dielectric material design.

This work addresses the modeling and simulation of strongly coupled electromagnetic and thermodynamic fields that arise in particulate-doped dielectrics using an adaptive staggered adaptive FDTD (finite difference time domain) method. Of particular interest is to provide a straightforward modular approach to finding the effective dielectric (electromagnetic) response of a material, incorporating thermal effects, arising from Joule heating, which alter the pointwise dielectric properties such as the electric permittivity, magnetic permeability, and electric conductivity. This is important for “thermal (damage) management” of materials used in electromagnetic applications. Because multiple field coupling is present, a staggered, temporally-adaptive scheme is developed to resolve the internal microstructural electric, magnetic and thermal fields, accounting for the simultaneous pointwise changes in the material properties. Numerical examples are provided to illustrate the approach. Extensions to coupled chemical and mechanical fields are also provided.

The rapid testing of red blood cell (RBC) volume fraction (“hematocrit”) is becoming increasingly important to identify blood disorders (“hemoglobinopathies”). Electromagnetic techniques provide an advantageous way to measure blood properties, primarily because they are inexpensive, quick and noninvasive. The goal of this paper is to develop estimates of the RBC volume fraction levels of whole blood from macroscopic electromagnetic (permittivity) measurements. The approach taken is to generate volume fraction estimates by inverting classical bounds on the effective permittivity of dielectric mixtures. The usefulness of the approach is that, given the permittivities of the plasma (known), cells (known) and whole mixture (measured), one can determine the cell volume fraction and compare it to the levels found in healthy blood. The deviation of the properties can be used to help characterize certain blood disorders. The expressions developed are not limited to RBC measurement, and are applicable to any cell-in-solution system. Through correlation of our laboratory measurements, the analytical expressions and direct large-scale numerical simulations, the results suggest that RBCs form high-permittivity cell-networks by making cell-to-cell contact, even at relatively low volume fraction.

The primary objective of this communication is to qualitatively describe charged wall growth in channel flow. The reduction of channel flow cross-section is often attributed to microscale suspensions and dissolved minerals which adhere to the flow boundaries (walls). In this analysis, the wall is comprised of an electrically conductive material, capable of carrying a charge. The flowing fluid, containing ions, is also assumed to be capable of carrying a charge. The resulting electrical field can be determined using Gauss’ law, which allows the associated electrical force to be computed at the solid–fluid interface. This force can impede or enhance the attachment of suspensions to the wall. Thus, there are two effects that play a role at the charged solid–fluid interface/wall: (1) mechanical shear due to the fluid flow and (2) an electrical force. It is the goal of this communication to develop a relationship that characterizes both contributions and to ascertain how this relationship scales with wall growth.

In many materials, strong electrical fields can cause highly conductive pathways to occur due to dielectric breakdown, which can cause the material to “jump” to a higher permittivity state. This effect is often undesirable and can lead to electrically-induced failure of a device, for example due to overheating. The overall goal of this work is to estimate the volume fraction and properties of the particulate additives needed to reduce the electrical load carried by a bulk material, in order to avoid dielectric breakdown.

A central issue in the use of ballistic fabric shielding is the mode of attachment to the structure that it is intended to protect. In order to investigate this issue, a discrete multi-scale yarn-network model is developed for structural fabric undergoing ballistic impact, based on work found in Zohdi and Powell [Zohdi TI, Powell D. Multiscale construction and large-scale simulation of structural fabric undergoing ballistic impact. Comput Meth Appl Mech Eng 2006;195:94–109] and Zohdi [Zohdi TI. Modeling/simulation of progressive penetration of multilayered ballistic fabric shielding. Comput Mech 2002;29:61–7]. The model is comprised of a network of yarn with stochastic properties determined by smaller-scale fibrils, which are randomly misaligned. The effects of stochasticity on the overall response are explored, and the model is compared against macro-scale experiments. The key feature of the model is the fact that it does not depend on phenomenological parameters, and can be calibrated by simply measuring the properties of an individual, smallest-scale, fibril. The properties of a fibril are easily ascertained from a simple tension test. The response of the overall fabric model and ballistic experiments are in excellent agreement. The model indicates that fabric which is attached by being pinned at the corners generally absorbs more energy, relative to fabric clamped along the sides. The basis for this result is discussed at length in the body of this work. Furthermore, it is observed that a uniform-yarn model, one which ignores the stochastic nature of the yarn, over-estimates the amount of energy absorbed.

In this work, a yarn-level computational model is used to predict the stress around flaws of varying shapes and sizes in sheets of structural fabric. The stress concentration is shown to depend solely on the size of the flaw along each of the primary yarn directions. Furthermore, the stresses in the fabric are seen to be very sensitive to the boundary conditions applied to the sheet.

In this work, we provide an introduction to an emerging field which has recently received considerable attention, namely the analysis and modeling of swarms. In a very general sense, the term swarm is usually meant to signify a group of objects (agents) that interact with one another and have a collective goal. Point-mass, particulate-like models are frequently used to simulate the behavior of groups comprised of individual units whose interaction are represented by inter-particle forces. The interaction “forces” can represent, for example in the case of Unmanned Airborne Vehicles (UAVs), motorized propulsion arising from inter-vehicle communication and then actuation resulting in thrust. For a swarm member, these forces have two main components, attraction and repulsion, with the fellow swarm members and the surrounding environment. This work develops and investigates (1) basic models of such systems, (2) properties of swarm models and (3) numerical algorithms, in particular temporally adaptive methods, for swarm-like systems.

We discuss computation of compliance/stiffness contribution tensors of an inhomogeneity of non-ellipsoidal shape and the difficulties that may be encountered in this context. These issues are illustrated on the example of one specific shape factor: concavity–convexity of the inhomogeneity shape. It is found, in particular, that the effect of the concavity factor depends on the specific constraint imposed. If the inhomogeneity volume is kept constant, then its compliance contribution rapidly increases with increasing concavity; on the computational side it leads to difficulties related to unusually high requirements to the accuracy of the computed volume averages quantities. If, on the other hand, the characteristic dimensions (for example, the distance between the farthest points) are kept constant, then the dependence of the compliance contribution on the concavity factor is almost linear.

This paper investigates the effective energy reflectance of materials comprised of a continuous matrix embedded with fine-scale particles of different electric permittivity and magnetic permeability. The specific objective is to determine under what conditions will increasing the particulate volume fraction initially increase (or decrease) the overall reflectance from a pure-matrix base state and, with further increase in volume fraction, reverse the trend, i.e. decrease (or increase) the effective reflectance. The importance of this condition is that it indicates when the correlation of a specific level of reflectance to a specific volume fraction of particles may not be unique, even when the properties of the particles and matrix are fixed.

The present work develops a flexible and robust solution strategy to resolve coupled systems comprised of large numbers of flowing particles embedded within a fluid. A model problem, consisting of particles which may undergo inelastic collisions in the presence of near-field forces, is considered. The particles are surrounded by a continuous interstitial fluid which is assumed to obey the compressible Navier–Stokes equations. Thermal effects are also considered. Such particle/fluid systems are strongly coupled, due to the mechanical forces and heat transfer induced by the fluid onto the particles and vice-versa. Because the coupling of the various particle and fluid fields can dramatically change over the course of a flow process, a primary focus of this work is the development of a recursive ‘‘staggering’’ solution scheme, whereby the time-steps are adaptively adjusted to control the error associated with the incomplete resolution of the coupled interaction between the various solid particulate and continuum fluid fields. A central feature of the approach is the ability to account for the presence of particles within the fluid in a straightforward manner that can be easily incorporated within any standard computational fluid mechanics code based on finite difference, finite element or finite volume type discretization. A three dimensional example is provided to illustrate the overall approach. � 2007 Elsevier B.V. All rights reserved.

The tremendous increase in accessible, powerful, desktop computers has raised the possibility of rapid high speed simulation of the response of fibrous biological tissue using networks of fibers to represent the load bearing component of such materials. The purpose of this paper is to present a relatively simple, robust, modeling and computational framework, based on fiber networks, which can be implemented with minimal effort by researchers in the biomechanics community, and which is relatively easy to tailor to specific applications. The advantages of such a fiber network approach are (1) the simplicity of the constitutive laws at the fiber level, for example relaxed one-dimensional Fung material laws, (2) the ability to easily incorporate effects such as fiber damage and rupture and (3) the amenability of the model to extremely rapid numerical simulation.

The purpose of this note is to highlight a new point of concern in the use of hypo-elastic constitutive equations. In particular, it is shown that if there is any uncertainty in the material constants that appear in such equations, it can induce nonmonotone uncertainty growth in the resulting solutions.

The focus of this work is the investigation of the overall scattering behavior of light by aggregates of randomly distributed particles. Specifically, a ray-tracing algorithm is developed and combined with a stochastic genetic algorithm in order to treat coupled inverse optical scattering formulations, where physical parameters, such as particulate volume fractions, refractive indices and thermal constants, are sought so that the aggregate response will match specified coupled scattering, thermal and infrared responses. Large-scale numerical simulations are presented to illustrate the overall procedure and to investigate the propagation through disordered particulate systems.

Certain classes of new lightweight structural fabric, primarily used for ballistic shielding, possess a multiscale structure constructed from microscale fibrils, which are bundled together to form yarn. The yarn are tightly woven into sheets. Since experimental ballistic tests for the evaluation, design and optimization of such materials are extremely expensive and time consuming, it is advantageous to develop models amenable to rapid computational methods. The purpose of the present work is to develop an efficient computational strategy in order to rapidly construct and numerically simulate multiscale representations of this class of materials. Large-scale simulations are presented to illustrate the potential of the approach in delivering realistic responses, involving dynamic penetration of a new lightweight structural fabric.

Experimental evidence suggests that, for materials exhibiting no appreciable work hardening and containing no more than approximately 20% volume fraction of pores, the macroscopic strain at which yield occurs is nearly constant, with a tendency to increase slightly as porosity increases. The present work shows that both observations - approximate constancy of strain at yield and its tendency to increase with porosity - have a relatively simple micromechanical explanation.

A wide range of modern applications have emerged where a successful analysis requires the simulation of flowing granular media which simultaneously incorporates near-field interaction between charged particles and intergranular contact. Such systems naturally arise in powder processing, micro- and nanotechnology, as well as in applications arising from the study of aerosols, epitaxy and astro- and geophysics. The focus of this communication is to develop models and physically-based high-performance solution strategies for the direct rapid simulation of such flowing granular media.