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In this paper we investigate topics related to the numerical simulation of the testing of mechanical responses of samples of microheterogeneous solid material. Consistent with what is produced in dispersion manufacturing methods, the microstructures considered are generated by randomly distributing aggregates of particulate material throughout an otherwise homogeneous matrix material. Therefore, the resulting microstructures are irregular and non-periodic. A primary problem in testing such materials is the fact that only finite-sized samples can be tested, leading to no single response, but a distribution of responses. In this work, a technique employing potential energy principles is presented to interpret the results of testing groups of samples. Three-dimensional numerical examples employing the finite element method are given to illustrate the overall analysis and computational testing process. Copyright © 2001 John Wiley & Sons, Ltd.

In this paper, we propose a simple computational framework for the rapid simulation of the delivery of substances into cells. Our approach treats the substances and the cell membrane as a collection of particles forming a discrete dynamical system, which is described by Newtonian equations in a purely mechanistic way. Detailed aspects about the modeling of particle interactions are discussed and resolved. The main advantage of such an approach is that it can offer a good qualitative picture of the delivery mechanism without the need to resort to detailed descriptions of the complex intermolecular interactions that are observed at small scales of the cell membrane. A numerical time integration scheme is formulated for solution of the system dynamics, and examples of simulations are provided. Computational particle-based models render reliable and fast simulation tools. We believe they can be very useful to help advance the design of delivery systems.

In this paper a coupled thermodynamical/chemical/mechanical model is developed to simulate the time dependent degradation of heterogeneous solid materials subjected to corrosive environments. The model, which is based on a description of the microscale, employs the first law of thermodynamics, a mass balance of a diffusing corrosive species, and a balance of momentum. The presence of the corrosive species is phenomenologically modeled as irreversibly reducing the material stiffness, dependent on the amount and time present. Numerical experiments are given to illustrate some characteristics of the model.

In this work variational bounds are developed on the difference between the solutions of two boundary-value problems involving linearly elastic material microstructure. Both problems have the same external geometry, boundary conditions and loading, however, one possesses no microstructure, i.e., it is homogeneous, while the other is “perturbed” with inhomogeneities. The bounds developed are solely in terms of the solution to the easier homogeneous material problem, the microstructure of the inhomogeneous problem and the given loading data. There are no unknown constants in the bounds. Furthermore, no calculation of the harder, typically intractable, inhomogeneous material problem is necessary. The bounds developed are obtained under no assumptions on the character of the microstructure of the inhomogeneous material problem, other than it be pointwise positive-definite, as well as under no assumptions on the external loading and geometry.

A model for the pressure-dependent diffusion and accumulation of hydrogen ahead of a decohesive intergranular crack front is developed. In the model, the pressure dependency of the diffusion is incorporated into the activation energy of an Arrhenius form of the material diffusivity along high-diffusivity grain boundaries. A key feature of the model is the ability to describe the trapping of hydrogen ahead of a decohesive crack front, which is observed in laboratory experiments.

A model introducing cohesive zones around material interfaces to simulate interfacial damage in microheterogeneous materials is developed. The material behavior within the cohesive zones is unknown a-priori, and is weakened, or "relaxed", on the continuum level from an initially undamaged state, by a reduction of the spatially variable elasticity tensor's eigenvalues. This reduction is initiated if constraints placed on the microstress fields, for example critical levels of pressure or deviatoric stresses, are violated. Outside of the cohesive zones the material is unaltered. Numerical computations are performed, employing the finite element method, to illustrate the approach in three dimensional applications.

On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, one can only test finite-sized samples. The macroscopic responses computed from various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncertainty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin functions, and others, employ predetermined linear elastic coefficients in parts of their representations. Therefore, they will contain the mentioned uncertainties. In this work we study the magnitude of deviations between computed homogenized linearly elastic responses among equal finite sized, samples possessing random microstructure. Afterwards, the sensitivity of finite deformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from above.

A domain decomposition methodis developed to reduce the computational complexity of boundary value problems associated withthe structural analysis of bodies with arbitrary external geometry, loading and linearly elasticmicrostructure. The purpose of the method is to augment existing numerical discretizationmethods of analysis, such as the finite element method. The approach is to partition and decouplethe heterogeneous body into more computationally tractable, nonoverlapping, subdomains whoseunion forms the entire domain under analysis. This is achieved by approximating the subdomainboundary conditions. The approximate boundary conditions, of displacement or traction type, aresupplied from the solution to a relatively computationally inexpensive auxiliary boundary valueproblem characterized by a simple regularized microstructure. Since the decoupled subdomainsmay then be analyzed separately, the memory requirements are reduced and computingprocedures are trivially parallelizable. A-posteriori error bounds are developed for solutionsgenerated by this process. It is shown that, in the special case of uniform exterior loading, theerror bounds collapse into forms which imply results pertaining to effective property orderingcoinciding with those published by Huet (1990) .

Summary. The effects of internal microstress fields are neglected in a usual simulation of the diffusion of a small solute trough solid heterogeneous media. However, when a heterogeneous material is used in a structure undergoing external mechanical loading, highly nonuniform stress fields can arise locally due to the variable microstructure. In this paper a simple quasi-Fickian model is studied which employs a spatially variable stress-dependent diffusivity, D ~. The structure of D ~ stems from an assumption that the stresses nonuniformly open and close the pores of the material microstructure, thus providing preferential sites for accumulation of the diffusing solute. When o- 0, the usual stress-free Fickian diffusivity, D ~ is recovered. Because of the highly oscillatory stress fields on the micro level, when employing numerical methods, such as the finite element or finite difference method, the distance between discretization nodes must be far smaller than the microstructural oscillations to obtain accurate simulations. This fact makes direct numerical simulations involving D ~ virtually impossible without computationally intensive, and complicated, special techniques. In this paper upper bounds are developed for the difference between solutions produced when using D ~ and alternatively D o in the body under analysis. The general case, when D ~ ~ and consequently D ~, are spatially variable, is considered. The bounds are a function of only D O and (7 and do not require any knowledge of the stress-dependent solution, and can thus be used as an a-priori check to determine whether potentially expensive computations are necessary.

Computational simulations of interacting microstructure in solid structures, with methods such as the finite element method, require solutions to numerically enormous boundary value problems. The primary objective of this work is to introduce a-posteriori error bounds for a domain decomposition which can be used to reduce the computational complexity of boundary value problems associated with such simulations. The approach is to partition and decouple the heterogeneous body into more computationally tractable, nonoverlapping, subdomains whose union forms the entire domain under analysis. This is achieved by computing a relatively inexpensive auxiliary „decoupling problem” with regularized coefficients but with the same external geometry and loading as the original body. The solution to the decoupling problem is then used to construct local boundary data for the subdomains, which can thereafter be solved independently, possibly in parallel.

In this paper a exible model for the description of damage in heterogeneous structural materials is presented. The approach involves solving the equations of equilibrium, with unilateral constraints on the maximum attainable values of selected internal variables. Due to the unilateral constraints, the problem is non-linear. Accordingly, a simple iterative algorithm is developed to solve this problem by (1) computing the internal elds with the initial undamaged microstructure and (2) reducing the material stiness at locations where the constraints are violated. This process is repeated until a solution, with a corresponding microstructure, that satises the equations of equilibrium and the constraints, is found. The corresponding microstructure is the nal ‘damaged’ material. As an application, the method is used in an incremental fashion to generate response curves describing the progressive macroscopic damage for a sample of commonly used bre-reinforced Aluminum=Boron composite. The results are compared to laboratory experiments published by Kyono et al. 1 and computational results using standard numerical methods, published by Brockenbrough et al. 2 ? 1998

In this paper, we develop a theory and methodology for obtaining approximate solutions to boundary value problems describing the deformation of highly heterogeneous linearly-elastic structures. The method, which represents a significant departure from traditional homogenization methods, provides a systematic and rigorous approach towards resolving the effects of microstructure of different scales on the macroscopic response of complex heterogeneous structures. An early variant of this method was first introduced in [IO]. The method, referred to as HDPM (Homogenized Dirichlet Projection Method), proceeds by first solving an auxiliary homogenized boundary value problem, describing the deformation of a structure with the same exterior geometry, but with a selected set of uniform material properties. The adequacy of this homogenized solution is then determined using an a posteriori error estimate that provides a measure of the error of the homogenized solution in subdomains of the structure compared to the solution of the fine-scale heterogeneous problem, without specific knowledge of this fine-scale solution. In those subdomains where the homogenized solution is deemed acceptable, it is retained. However, in subdomains where the homogenized solution is inadequate, as is determined when the estimated error exceeds a preset tolerance, a local boundary value problem is constructed by projecting the homogenized displacements onto a partition designed to isolate these subdomains. These local boundary value problems are then solved in those subdomains where the homogenized solution is inaccurate using the exact microstructure with the approximate local boundary conditions. A posteriori error estimates are made to ascertain the quality of the resulting solution. If the quality of the solution remains inadequate, above a preset error tolerance, a two stage adaptive procedure is implemented. Stage-I (‘material adaptivity’) corresponds to modifying the homogenized structure’s material properties. If, after Stage I, the solution quality is still inadequate, the subdomains of local solution are enlarged, thereby modeling in greater detail the actual microstructure, and the local solution process is. repeated (Stage-II, ‘subdomain unrefinement’). The main feature of this method is that only in subdomains where the error in the usual homogenized solution is above a preset tolerance is the microstructure taken into account. The cost of this method is shown to be orders of magnitude cheaper than direct huge-scale computational simulations of micromechanical events. The results of several numerical experiments are provided to demonstrate the method and verify theoretical estimates. In this work, we present a method for the solution of boundary value problems modeling the deformation of structures composed of highly heterogeneous linearly-elastic materials. We concentrate on materials formed by a homogeneous matrix embedded with particulate matter of different properties (Fig. 1). However, the results presented are not limited to materials of this type, and can, in theory, be used for materials with virtually any microstructure. A straightforward calculation reveals that an accurate numerical approximation of fine-scale solutions of

Particulate media are ubiquitous in modern manufacturing processes. These include spray-forming, abrasive finishing, and sintering based processes amongst others. All of these processes involve a flowing stream of discrete, particulate media. For these processes, the aggregate behavior originating from the individual particle or grain dynamics is of critical importance from a process engineering perspective. The discrete nature of the media poses unique challenges in formulating direct continuum theories. This motivates investigating appropriate discrete computational techniques. In this paper, we present a computer simulation framework based on collision driven particle dynamics to investigate the engineering of such manufacturing processes. This is part of an ongoing work on developing a general-purpose computer simulation tool to analyze the dynamics of particulate and granular media in engineering applications. This paper presents the overall framework and the underlying physical models. In particular, our focus is on modeling individual particle-based phenomena (including collisions, heat-exchange, and energy loss) and deriving the aggregate response of the media from individual particle dynamics. The technique is demonstrated using a numerical example for a spray coating deposition process. This example tracks the particulate behavior from the nozzle opening downstream until impact with substrate. Such investigations are useful to understand the effect of process parameters on the engineered output — which in this case entails the properties of the surface coating. The simulation is found to be reasonable in performance time.Copyright © 2013 by ASME

In many small-scale devices, the materials employed are functionalized (doped) withmicroscale and/or nanoscale particles, in order to deliver desired overall dielectric prop-erties. In this work, we develop a reduced-order lumped-mass model to characterize thedynamic response of a material possessing a microstructure that is comprised of anelectromagnetically-neutral binder with embedded electromagnetically-sensitive(charged) particles. In certain industrial applications, such materials may encounterexternal electrical loading that can be highly oscillatory. Therefore, it is possible for theforcing frequencies to activate the inherent resonant frequencies of these micro- andnanostructures. In order to extract qualitative information, this paper first analyticallyinvestigates the mechanical and electromagnetic (cyclotronic) contributions to thedynamic response for a single particle, and then quantitatively investigates the responseof a model problem consisting of a coupled multiparticle periodic array, via numericalsimulation, using an implicit temporally-adaptive trapezoidal time-stepping scheme. Forthe model problem, numerical studies are conducted to observe the cyclotronically-dominated resonant frequency and associated beat phenomena, which arises due to thepresence of mechanical and electromagnetic harmonics in the material system.[DOI: 10.1115/1.4023251]Keywords: particulate composites, electromagnetics, vibration

In virtually every modern engineering design, new composite particulate materials are employed that are specifically tailored to the application at hand. These materials are constructed by combining an easy to form matrix-binder material with embedded particles, whose properties are chosen to deliver overall desired properties. Trial and error experiments to determine the correct combinations of such materials are tedious and expensive. Accordingly, over the past century, methods have been developed to accelerate the process of material design by attempting to reliably estimate the effective responses of such materials in terms of the material properties of the matrix material, the properties of the particulate additives, and the volume fraction of the particulate additives. This chapter provides a basic overview of some straightforward analytical methods used in such analyses. Keywords: particulate composites; property estimates

Many modern materialsare comprised of an assembly of various microscale components, typically ground up particulates or fibers in a binding matrix which is formed into engineering geometries.

In this paper, a methodology is introduced for the development of adaptive methods for hierarchical modeling of elastic heterogeneous bodies. The approach is based on the idea of computing an estimate of the modeling error introduced by replacing the actual fine-scale material tensor with that of a homogenized material, and to adaptively refine the material description until a prespecified error tolerance is met. This process generates a family of coarse-scale solutions in which the solution corresponding to the fine-scale model of the body, which embodies the exact microstructure, loading and boundary conditions, represents the highest level of sophistication in a family of continuum models. The adaptive strategy developed can lead to a new non-uniform description of material properties which reflects the loading and boundary conditions. A post-processing technique is also introduced which endows the coarse-scale solutions with fine-scale information, through a local solution process. Convergence of the adaptive algorithm is proven and modeling error estimates as a function of scale of material description are presented. Preliminary results of several numerical experiments are given to confirm estimates and to illustrate the promise of the approach in practical applications.

In this paper, a mathematical model is developed to qualitatively simulate the progressive time-evolution of a blast from a simple firework. Estimates are made for the blast radius that one can expect for a given amount of detonation energy and pyrotechnic display material. The model balances the released energy from the initial blast pulse with the subsequent kinetic energy and then computes the trajectory of the material under the influence of the drag from the surrounding air, gravity and possible buoyancy. Under certain simplifying assumptions, the model can be solved for analytically. The solution serves as a guide to identifying key parameters that control the evolving blast envelope. Three-dimensional examples are given.

Cardiac growth and remodeling in the form of chamber dilation and wall thinning are typical hallmarks of infarct-induced heart failure. Over time, the infarct region stiffens, the remaining muscle takes over function, and the chamber weakens and dilates. Current therapies seek to attenuate these effects by removing the infarct region or by providing structural support to the ventricular wall. However, the underlying mechanisms of these therapies are unclear, and the results remain suboptimal. Here we show that myocardial infarction induces pronounced regional and transmural variations in cardiac form. We introduce a mechanistic growth model capable of predicting structural alterations in response to mechanical overload. Under a uniform loading, this model predicts non-uniform growth. Using this model, we simulate growth in a patient-specific left ventricle. We compare two cases, growth in an infarcted heart, pre-operative, and growth in the same heart, after the infarct was surgically excluded, post-operative. Our results suggest that removing the infarct and creating a left ventricle with homogeneous mechanical properties does not necessarily reduce the driving forces for growth and remodeling. These preliminary findings agree conceptually with clinical observations. © 2012 Elsevier Ltd. All rights reserved.

Heterogeneous microstructures lead to a distortion of the electrical and current field within the material mixture. This leads to the fields becoming amplified within the material, which can lead to a variety of detrimental effects. An important quantity of interest is the amount of heat generated from an electrical field. The interconversions of various forms of energy (electromagnetic, thermal, etc.) in a system are governed by the first law of thermodynamics (which will be derived in detail shortly)

In order to properly consider multifield coupling effects, we will need to draw on some of the tools of classical continuum mechanics.

Some fundamental definitions and observations in conjunction with electromagnetic phenomena are

We now consider the next level of complexity beyond rigid clusters of particles, namely, free-flowing systems of charged particles. Furthermore, we consider thermal effects in such systems, which partially arise due to interparticle impact, as well as contact with the external environment, i.e., obstacles.

It has long been recognized that interactive cooperative behavior within biological groups or “swarms” is advantageous in avoiding predators or, vice versa, in capturing prey. For example, one of the primary advantages of a swarm-like decentralized decision making structure is that there is no leader and thus the vulnerability of the swarm is substantially reduced. Furthermore, the decision making is relatively simple and rapid for each individual, however, the aggregate behavior of the swarm can be quite sophisticated.

In closing, we discuss emerging applications in bioelectromagnetics to Red Blood Cells (RBCs), which are responsible for the transport of oxygen and carbon dioxide, and are the most prevalent type of cells in human blood. The average cellular volume of each cell (82-96 femtoliters) is occupied by a high concentration of the oxygen carrying protein hemoglobin at a concentration of 30-36 %. The lifespan of the human RBCs is approximately 120 days after they are released from the bone marrow as reticulocytes. Typically 4-6 million RBCs per cubic millimeter occupy 41-52 % of blood volume (hematocrit). The typical biconcave shape of RBCs endows the cell with ideal deformability characteristics. This allows RBCs to efficiently perform their function in small capillaries. Alterations in RBC properties, including shape, volume and membrane characteristics will lead to a decreased lifespan and when not compensated by increased production, a lower volume and anemia. Genetic disorders in cytoskeletal proteins (the cell wall “scaffolding”) results in RBC pathologies, such as hereditary spherocytosis and hereditary elliptocytosis (Eber and Lux [22], and Gallagher, [31] and [32]). Deviations in cytosolic and membrane proteins may affect the state of hydration of the cell and thereby its characteristics. Figure 10.1 illustrates some examples of unhealthy cell morphologies. In normal blood, echinocytes and stomatocytes can be observed, in addition to discocytes. Acanthocytes are observed in acquired hepatic syndromes, codocytes are found in thalassemia. In sickle cell disease, hemoglobin polymers will distort the shape of the cell and drepanocytes are observed. Elliptocytes are the result of membrane disorders where interactions in the horizontal direction (e.g., spectrin-spectin interactions) are disrupted, and spherocytes are observed in membrane disorders where the interaction between the lipid bilayer and the underlying membrane skeleton is dysfunctional. The number of humans that are affected by Sickle cell disease, Thalassemia and other hemoglobinopathies, runs in the millions (Forget and Cohen [29] and Steinberg et al. [97]). Such disorders lead to altered hemoglobin and result in changes in RBC properties, which is related to blood pathology, including anemia.

An important issue that this monograph addresses is the modeling and simulation of strongly coupled electromagnetic and thermodynamic fields that arise in particulate-doped dielectrics using an adaptive staggered 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. Here, we follow an approach found in Zohdi [139].

We start with an introduction to the dynamics of a single charged particle, and then progress to rigid clusters, and then flowing systems.

Most modern electromagnetic devices owe a significant amount of their success to the tailored electromagnetic material behavior of the components that comprise them. A relatively inexpensive way to obtain macroscopically desired responses is to enhance an easy-to-form matrix material’s properties by introducing microscale particles possessing different electromagnetic, thermal and mechanical properties. (Figure 1.1). The particles are chosen to produce an overall desired electromagnetic effect. The aggregate response of the material is an outcome of the interaction between the smaller-scale (microstructure) constituents that comprise the “effective” material. In the construction of such materials, the basic philosophy is to select matrix/particle material combinations in order to produce desired aggregate responses. For example, in electromagnetic engineering applications, the classical choice is to add a particulate phase with suitable dielectric constants in order to modify the overall properties of an easily moldable base matrix material.

Here, we follow a recent analysis of Zohdi [4], the impact of particles on electrified surfaces has wide-ranging applications, for example, in coating technologies. A single particle impacting a surface will rebound according to the basic laws governing a conservation of linear momentum, in conjunction with restitution relations and friction laws.

In order to introduce fundamental concepts pertaining to effective properties of electromagnetic media, we initially start with static, lossless, conditions. Afterwards, we consider more general, thermally-sensitive, time-transient scenarios and the corresponding numerical methods.

In this work, boldface symbols imply vectors or tensors. A fixed Cartesian coordinate system will be used throughout this monograph. The unit vectors for such a system are given by the (fixed) mutually orthogonal triad ( e 1, e 2, e 3). For the inner product of two vectors, u and v, in three dimensions we have

Generally, methods for the time integration of differential equations falls within two broad categories: (1) implicit and (2) explicit. In order to clearly delineate between the two approaches, we first study a generic equation of the form (\({\emph \bf U}\)=unknown variable)

As the next level of complexity beyond the dynamics of a single particle, we consider rigid clusters of such particles. In this chapter, we consider the cluster to already be formed, with particles rigidly bound together by either mechanical, chemical or electromagnetic bonds.

We develop a novel patterning technique to create 3D patterns of micro, nanoparticle assembly via evaporative self-assembly based on confinement/release of micro/nano particles assembly based on the coffee-ring effect of evaporating suspension. Based on the presented technique, we demonstrate that the patterns of 3D assembly of various sizes of microparticles (Silica), metal oxide nanoparticles (TiO2, ZnO) and metallic nanoparticles (Ag) can be successfully generated by low-concentrated particle suspension (1.25 wt % ~ 5 wt %) without additional sintering steps and we also show the geometries of the patterns can be finely controlled by adjusting the parameters of the process.

From its inception, the field of computational mechanics has primarily been focussed on engineering applications involving solid and fluid mechanics. As we enter the 21st century, it is apparent that we enter a different period in human civilization where, perhaps, computational methods can also start to play a significant and constructive role. The recent dramatic increase in computational power available for mathematical modeling and simulation raises the possibility that numerical methods can play a significant predictive role in the analysis of populations. This fact has motivated the work that will be presented. As a model problem, the objective of this work is to begin the development of robust computational procedures to investigate the behavior of initially intermeshed hostile, potentially human, populations. The applications are numerous, stemming from human civil wars on the macroscale to cellular-level conflicts, for example, between cancer and healthy cells, on the microscale. Classical modeling approaches attempt to develop continuum type field equations, usually making somewhat unrealistic assumptions in order to obtain tractable partial differential equations. For example, when dealing with small populations, or populations which become quite small and heterogeneously dispersed during the time-history of interaction, the assumptions behind regularization techniques leading to continuum models, may not apply. With these issues in mind, and due to the dramatic increase in desktop computing, we develop a discrete interaction approach where one can easily modify “rules of engagement”, population sizes, reproductive rates, etc, to provide quantitative spatial and temporal information. A robust inverse algorithm is also developed to determine “parity points”, i.e. multiple parameter sets which yield population coexistence. For sufficiently complex models of population interaction, the determination of parity points falls within the category of non-convex, non-differential optimization, with constraints. Accordingly, a general approach, based on a stochastic genetic algorithm, is developed and applied to a sufficient complex model for two interacting populations in order to illustrate the overall method.

Most finite element models of atherosclerotic arteries do not account for the heterogeneity of the plaque constituents at the microscale. Failure of plaque lesions has been shown to be a local event, linked to stress concentrations caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. There is growing evidence that microcalcifications exist in the fibrous cap of plaque lesions. However, their role is not yet fully understood. The goal of the present work is to investigate the effects of localized regions of microcalcifications on the stress field of atherosclerotic plaque caps in a section of carotid artery. This is achieved by performing finite element simulations of three-dimensional fluid-structure interaction models. The material response in the region of microcalcification is modeled using a combination of finite elements, homogenization theory, and a stress concentration function that approximates the average local stresses in the fibrous tissue and microcalcification phases. The results indicate that the circumferential stress in the fibrous tissue phase increases as the volume fraction of microcalcifications is increased, and that the stress exceeds a critical threshold when the fibrous cap thickness is decreased. Furthermore, the presence of the microcalcifications significantly influences the distribution of stress by shifting the maximum circumferential stress away from the cap shoulders, where failure is most common when the effective region of microcalcification is located at the center of the cap. This is a possible explanation of why 40% of plaque ruptures occur away from the shoulder region of the cap.

An investigation is conducted of the stress-assisted grain-boundary diffusion of hydrogen in Al-Li alloys, with a view to the characterization of the intergranular embrittlement mechanism. A comparison of theoretical predictions with experimental observations indicates that intergranular hydrogen embrittlement involves the nucleation of an incremental crack at the edge of the plastic zone that extends not only backwards, to join the original crack, but also forwards: in a region that is stressed above a critical level and has a rather elevated hydrogen concentration. Crack jump distance predictions are in excellent agreement with experimental observations; ligament fracture is the step controlling the hydrogen-embrittlement fracture process. 17 refs.

We developed an ultrafast microfluidic approach to self-assemble microparticles in threedimensions by taking advantage of simple photolithography and capillary action of microparticle-dispersed suspensions. The experimental verifications of the assembly of various sizes of silica microspheres and silica gel microspheres within thin and long open microchannels by using this approach have been demonstrated. We anticipate that the presented technique will be widely used in semiconductor and Bio-MEMS (microelectromechanical Systems) fields because it offers a fast way to control 3D, microscale particle assemblies and also has superb compatibility with photolithography, which can lead to an easy integration of particle assembly with existing CMOS (complementary metal-oxide-semiconductor) and MEMS fabrication processes.

In this work a multibody collision model, ame-nable to large-scale computation, is developed to simulate material removal with particulate flows. This model is developed by computing momentum exchange to account for different force interactions: (1) particle–particle interaction, (2) particle–fluid interaction, and (3) particle–surface interaction. For the particle-fluid interaction, a velocity field for the fluid is assumed to be known, and the drag force on the particles is computed from this field. In the particle–surface interaction, the Boussinesq solution for a point load on an elastic half-space is used along with the von-Mises yield criterion to determine the amount of material removed. Employing this model, inverse problems are then constructed where combinations of the abrasive particle size, the particle size distribution, the flow velocity, etc., are sought to maximize the efficiency of the process. A genetic algorithm is used to treat this inverse problem, and numerical examples are given to illustrate the overall approach.