Double and multiple contacts of similar elastic materials

Sundaram, Narayan K Purdue University 2009 해외박사(DDOD)

Ongoing fretting fatigue research has focussed on developing robust contact mechanics solutions for complicated load histories involving normal, shear, moment and bulk loads. For certain indenter profiles and applied loads, the contact patch separates into two disconnected regions. Existing Singular Integral Equation (SIE) techniques do not address these situations. A fast numerical tool is developed to solve such problems for similar elastic materials for a wide range of profiles and load paths including applied moments and remote bulk-stress effects. This tool is then used to investigate two problems in double contacts. The first, to determine the shear configuration space for a biquadratic punch for the generalized Cattaneo-Mindlin problem. The second, to obtain quantitative estimates of the interaction between neighboring cylindrical contacts for both the applied normal load and partial slip problems up to the limits of validity of the halfspace assumption. In double contact problems without symmetry, obtaining a unique solution requires the satisfaction of a condition relating the contact ends, rigid-body rotation and profile function. This condition has the interpretation that a rigid-rod connecting the inner contact ends of an equivalent frictionless double contact of a rigid indenter and halfspace may only undergo rigid body motions. It is also found that the ends of stick-zones, local slips and remote-applied strains in double contact problems are related by an equation expressing tangential surface-displacement continuity. This equation is essential to solve partial-slip problems without contact equivalents. Even when neighboring cylindrical contacts may be treated as non-interacting for the purpose of determining the pressure tractions, this is not generally true if a shear load is applied. The mutual influence of neighboring contacts in partial slip problems is largest at small shear load fractions. For both the pressure and partial slip problems, the interactions are stronger with increasing strength of loading and contact proximity. A new contact algorithm is developed and the SIE method extended to tackle contact problems with an arbitrary number of contact patches with no approximations made about contact interactions. In the case of multiple contact problems determining the correct contact configuration is significantly more complicated than in double contacts, necessitating a new approach. Both the normal contact and partial slip problems are solved. The tool is then used to study contacts of regular rough cylinders, a flat with rounded punch with superimposed sinusoidal roughness and is also applied to analyze the contact of an experimental rough surface with a halfspace. The partial slip results for multiple-contacts are generally consistent with Cattaneo-Mindlin continuum scale results, in that the outermost contacts tend to be in full sliding. Lastly, the influence of plasticity on frictionless multiple contact problems is studied using FEM for two common steel and aluminum alloys. The key findings are that the plasticity decreases the peak pressure and increases both real and apparent contact areas, thus 'blunting' the sharp pressures caused by the contact asperities in pure elasticity. Further, it is found that contact plasticity effects and load for onset of first yield are strongly dependent on roughness amplitude, with higher plasticity effects and lower yield-onset load at higher roughness amplitudes.

Foundations of computational geometric mechanics

Leok, Melvin California Institute of Technology 2004 해외박사(DDOD)

Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Computational algorithms obtained from a discrete Hamilton's principle yield a discrete analogue of Lagrangian mechanics, and they exhibit excellent structure-preserving properties that can be ascribed to their variational derivation. We construct discrete analogues of the geometric and symmetry methods underlying geometric mechanics to enable the systematic development of computational geometric mechanics. In particular, we develop discrete theories of reduction by symmetry, exterior calculus, connections on principal bundles, as well as generalizations of variational integrators. Discrete Routh reduction is developed for abelian symmetries, and extended to systems with constraints and forcing. Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute. In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincare lemma are introduced, and their discrete properties are analyzed. In examples such as harmonic maps and electromagnetism, discretizations arising from discrete exterior calculus commute with taking variations in Hamilton's principle, which implies that directly discretizing these equations yield numerical schemes that have the structure-preserving properties associated with variational schemes. Discrete connections on principal bundles are obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition that takes into account the principal bundle structure is introduced. Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques. Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature. Explicit expressions for Lie group, higher-order Euler-Poincare, higher-order symplectic-energy-momentum, and pseudospectral variational integrators are presented, and extensions such as spatio-temporally adaptive and multiscale variational integrators are briefly described.

Microstructural mechanics of collagen gels and tissue equivalents

Chandran, Preethi Lourdes University of Minnesota 2005 해외박사(DDOD)

This aim of this study was to correlate the macro-scale mechanics of a collagen gel to the kinematics at the microstructural level, and formulate a mathematical model that addressed both. Collagen gels, reconstituted in-vitro from type-1 collagen, are a useful model of tissue mechanics. The gel is comprised solely of collagen fibrils, a major mechanical component of soft tissues, and retains a large part of the in-vivo physiological character. Under the microscope, the gel appears a hydrated mesh of nearly straight fibrils. Confined compression experiments performed with simultaneous birefringence imaging suggested the fibrils to be interconnected. The bending of fibers (relative angle change) at interconnections and retardation by viscous drag was found responsible for the mechanics observed at the macro-scale. A network model of collagen gel mechanics was proposed. Traditional models of fibrous tissue neglect load transfer between fibrils (as occurs in a network) and approximate the kinematics of the independently-deforming fiber to be affine with the matrix. A simulation study was performed on a microstructure based on the collagen gel, and it was concluded that the computationally-attractive affine assumption could not capture network behavior. A multi-scale model of collagen-gel mechanics was proposed to the enable the study of macro-scale boundary value problems but with constitutive response determined at the micro-scale network level. The model was derived from ideas of Averaging theory and solved at the macro-scale using Finite Elements, and analyzed at the micro-scale using Representative Volume Elements. The mono-phasic model was able to predict key observations in a published study of tissue equivalents in uniaxial extension. A simplified wound mechanics problem was also simulated. To simulate gel behavior in confined compression, a biphasic version of the network model was derived. A microstructural representation of an elastic network, with elastic bending resistance, and retarded by a Stokes-like viscous drag was able to reproduce the behavior observed in the experimental study. This work contributes to the analysis of tissues where fibril-fibril load transfer is important. The insight into collagen gel micro-mechanics is a step towards deciphering the complex relation between microstructure and mechanical properties in real tissues.

Diffusion, Deformation, and Damage in Lithium-Ion Batteries and Microelectronics

Pharr, George Mathews, V Harvard University 2014 해외박사(DDOD)

This thesis explores mechanical behavior of microelectronic devices and lithium-ion batteries. We first examine electromigration-induced void formation in solder bumps by constructing a theory that couples electromigration and creep. The theory can predict the critical current density below which voids do not form. Due to the effects of creep, this quantity is found to be independent of the solder size and decrease exponentially with increasing temperature, different from existing theories. We then investigate the interplay between mass transport, deformation, stress, and fracture in lithium-ion battery electrodes. First, we model fracture of elastic electrodes by combining ideas from diffusion kinetics and fracture mechanics. Next, we examine mechanics of high-capacity lithium-ion batteries, which demonstrate inelastic deformation, by constructing a model that accounts for diffusion and elastic-plastic deformation. These models suggest that fracture is prevented in small and soft electrode materials that are cycled slowly. To investigate crystalline silicon electrodes, we construct a continuum model of concurrent reaction-controlled kinetics and plasticity. To quantify the kinetics of the lithiation process, we perform electrochemical experiments on crystalline silicon wafers of various orientations. Using the velocities measured in these experiments and our continuum model, we correctly predict anisotropic morphologies and fracture patterns developed in crystalline silicon nanopillars. We then measure the fracture energy of lithiated silicon, finding it to be similar to that of pure silicon and essentially independent of the lithium concentration. These findings demonstrate that lithiated silicon has a peculiar ability to flow plastically but fracture in a brittle manner. To investigate this interesting combination of properties, we measure stresses in silicon thin films as a function of charging rate. Increasing the rate of lithiation resulted in a corresponding increase in the flow stress, indicating rate-sensitive plasticity. Microelectronics and lithium-ion batteries are rich in mechanics, requiring considerations from large deformation, plasticity, creep, kinetics, and fracture mechanics. These systems involve an intimate coupling between mechanics and a number of other fields, such as chemical reactions, electric fields, mass transport, and electrochemistry. Thus, it is believed that this thesis will provide general insight into systems that involve coupling between mechanics and other disciplines.

Dynamic and quasi-static contact and scratch analysis of micro-nanoscale thin solid films with application to magnetic storage hard disk drives

Katta, Raja Ramakanth University of Illinois at Urbana-Champaign 2009 해외박사(DDOD)

With current demand for decreased size of micro/nanoscale systems, coupled with increased mobility, critical understanding of the ensuing contact or impact related behavior of thin solid films used in these systems is of paramount importance for improved design and reliability. In modern micro/nanodevice technologies significant emphasis has to be placed on the design of thin-films which can provide the required contact and scratch resistance. To aid this endeavor, scientific studies of the contact and scratch processes in these systems, both static and dynamic are needed to provide the tools necessary to help the advancement of these technologies. One such problem is the impact contact or quasi-static contact and scratch of the slider and disk in magnetic storage hard disk drives (HDD). Similar contact problems are encountered during the operation of other micromechanical systems like RF-MEMS switches where surface damage is observed after cyclic contact. One of the most critical elements of multilayer contact analysis is proper determination of the nanomechanical properties of each thin-film on the multilayer system. In the first part of this work the method of determining the mechanical properties using the Oliver and Pharr (O-P) nanoindentation technique is described. For nanometer sized thin-films where the O-P technique gives incorrect results, an improved method is used. Later a dimensional analysis-based method to obtain the mechanical properties from the nanoindentation data is implemented for magnetic storage films. A direct comparison of the properties obtained from conventional O-P nanoindentation technique to this new technique is presented. In the second part of this work, the effect of dynamic contact or impact on multilayer thin films specific to magnetic storage hard disk drives is presented. Since there are no impact models available for multilayer thin films in the literature, a new contact mechanics-based (CM) semi-analytical model of a rigid sphere (representing a slider corner) impacting an elastic-plastic (E-P) multilayer thin-film half-space was proposed for the first time to examine the potential damage to a magnetic storage head disk interface (HDI). A dynamic 3D finite element analysis (FEA) model was also developed to examine the impact damage in more detail and validate the impact model. To characterize the plastic deformation and frictional energy losses associated with the impact damage, a comprehensive oblique elastic impact coefficient of restitution (COR) model was proposed for elastic-plastic impacts for the first time and validated using FEA. A method to decouple the oblique impact parameters into normal impact COR and tangential impact COR was formulated. Since, in microsystems, the geometry of the impacting bodies is not limited to spherical bodies, a new contact mechanics-based (CM) model of a rigid cylinder with a finite length impacting an elastic-plastic homogeneous disk was also proposed and includes a novel method of estimating the residual depth after impact. Based on elastic unloading, an improved coefficient of restitution model was also proposed. This new impact model was applied to study a practical case of a cylindrical feature on the slider of a magnetic storage hard disk drive impacting the disk to predict various critical impact contact parameters. The CM model was validated using a plane strain FEA-based model and it was found that a cylindrical feature with longer length results in a substantial alleviation of impact damage. The final part of this work involved the investigation of the performance of thin-film multilayers while under the influence of much milder quasi-static contact scratch. A 2D plane strain FEA model of a rigid cylinder sliding over a multilayered thin-film half space was developed. The effects of different contact parameters such as applied normal load, friction coefficient and radius of curvature of the cylinder on the critical stresses in the multilayer system were analyzed. Later, for direct experimental comparison a full-blown 3D quasi-static FEA-based nanoscratch model of the multilayer thin-film system was also developed. The FEA scratch results were compared to nanoscratch experiments performed on actual magnetic disks. Consequently, the 3D FEA scratch model was used to quantitatively correlate the subsurface plastic deformation to the magnetic erasures typically found in HDDs due to scratch for the very first time.

Arbitrary Lagrangian-Eulerian (ALE) finite element formulations in finite strain elasto-plasticity

Love, Edward University of California, Berkeley 2000 해외박사(DDOD)

This dissertation presents a new implicit Arbitrary Lagrangian-Eulerian (ALE) finite element method for large deformation plasticity problems in solid mechanics. An extension to fluid dynamics is also included. The proposed formulation is based on a composition of mappings which does not appear to have been fully investigated or developed in previous works in this area. The first part of the dissertation presents the necessary background information on Lagrangian continuum mechanics and it's mixed finite element implementation. Both finite strain elasticity and multiplicative plasticity are considered. The latter includes constitutive models of inelastic solids based on the multiplicative decomposition <bold>F</bold> = <bold>F</bold><italic><super> e</super></italic><bold>F</bold><italic><super>p</super></italic> of the deformation gradient into an elastic and a plastic part, with the elastic response of the material given in terms of an elastic potential. These Lagrangian methods are to be extended to the ALE setting. Next, an existing ALE method is implemented and evaluated for reference and comparison purposes. The focus of this work is on implicit methods, with explicit schemes considered as a particular case. The second part of the dissertation focuses on the newly developed implicit ALE method. The proposed schemes are discussed first in the context of finite elasticity. They include both coupled and staggered solution strategies. The staggered scheme, in particular, involves a separate solution of the advection phase, leading to more computationally efficient procedures. The extension to plasticity problems is presented next. The advection of the internal variables is discussed in detail. The third part of the dissertation presents the extension of the new ALE method to solid dynamics. Furthermore, a viscous fluid can be viewed as a special case of a rigid-viscoplastic solid. This crucial observation leads to an easy extension of these developments to fluid dynamics problems. The interest in this work focuses on applications involving a contained fluid, typically with free surfaces or fluid/solid interfaces to be modeled accurately. The dissertation concludes with a discussion of the possible future lines of research after the identification of some outstanding issues in this area of computational mechanics. (Abstract shortened by UMI.).

Continuum mechanics modeling and experimental confirmation for the prediction of nanoscale transitional fracture behavior

Starr, Michael James The University of Wisconsin - Madison 2002 해외박사(DDOD)

A continuum mechanics-based model is used to explore the fracture properties of nanoscale multilayered materials. Length scale appears via inclusion of potential emission of discrete dislocations from a crack tip following the Rice-Thomson approach. For nanoscale multilayers, the high density of interfaces has a strong effect on the propensity for a crack to emit blunting dislocations, which relieve high local stresses, or not emit them, which promotes cleavage. The model is used to predict how material combination, layer thickness, crystal structure, and flaw size influence the effective fracture toughness of the material system for the “mesoscopic” size regime that bridges atomistics and continuum mechanics. To confirm validity of the continuum model at the nanoscale and test certain critical predictions, viz. the directions of dislocation emission from crack tips, Bragg bubble raft experiments are performed. Perfect (dislocation-free) two-dimensional bubble rafts with sharp internal and interfacial cracks are subjected to the bounding cases of uniform displacement or traction to examine the nucleation and emission of dislocations. The experiments verify, qualitatively and quantitatively, the trends predicted by the model. Theory and experiment demonstrate transitions in emission behavior that take place over a large range of crack dimensions, crack locations, and loading conditions. Remarkably, the continuum model is confirmed to predict the crack dislocation emission behavior down to length scales approaching several atomic (bubble) spacings. The continuum model is applied to materials and material systems to make predictions of nominal crack response as a function of specimen size and geometry. The model predicts substantial modifications to crack behavior on the nanoscale. Most notable are predictions of brittle-to-ductile transition in macroscopically brittle materials such as silicon and germanium. Finally, it is proposed that the theoretical model may have utility in making predictions of brittle-to-ductile transitions during precision machining operations involving nanoscale depths of cut. A preliminary investigation into an elastic cutting model, featuring a simple chip formation geometry, predicts a physical transition from purely elastic response to elastoplastic response in silicon and germanium on the nanoscale. These predictions exhibit intriguing consistency with experimental machining data.

Nonholonomic and discrete Hamilton-Jacobi theory

Ohsawa, Tomoki University of Michigan 2010 해외박사(DDOD)

The first part of the thesis discusses an extension of Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton---Jacobi theory does. We develop nonholonomic Hamilton-Jacobi theory from two different perspectives; one is a direct approach based on the standard formulation of nonholonomic systems, and the other uses the technique of the Chaplygin Hamiltonization. We also establish a link between these two approaches by providing an explicit formula that relates the solutions of the Hamilton-Jacobi equations resulting from both approaches. The second part of the thesis develops a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time, and is shown to recover the Hamilton-Jacobi equation in the continuous-time limit. The correspondence between discrete and continuous Hamiltonian mechanics naturally gives rise to a discrete analogue of Jacobi's solution to the Hamilton-Jacobi equation. We also prove a discrete analogue of the geometric Hamilton-Jacobi theorem. These results are readily applied to the discrete optimal control setting, and some well-known results in discrete optimal control theory, such as the Gellman equation (discrete-time Hamilton-Jacobi-Bellman equation) of dynamic programming, follow immediately. We also apply the theory to discrete linear Hamiltonian systems, and show that the discrete Riccati equation follows as a special case of the discrete Hamilton-Jacobi equation.

Synergy between chemical dissolution and mechanical abrasion during chemical mechanical polishing of copper

Che, Wei Iowa State University 2005 해외박사(DDOD)

Chemical mechanical planarization (CMP) is a mainstream semiconductor processing method for achieving local and global wafer planarization. However, the CMP process fundamentals are poorly understood, and thereby inhibit migratability of lab-scale experiments to production processes. This work addresses the synergistic role of chemical dissolution rate (CDR) and mechanical abrasion rate (MAR) on the material removal mechanisms during CMP process. A set of nano-wear experiments on elecro-plated copper surfaces are conducted with systematic exposure to active slurry. Initial results of in situ wear test in chemically active slurry showed an increased material removal rate (MRR) relative to a dry wear test. A phenomenological MRR model based on scratch-intersections was formulated to understand the role of consumables and the process parameters. To further understand the synergistic effects between CDR and MAR, two plausible mechanisms of material removal are investigated. Mechanism-I is based on chemical dissolution enhancing MAR. A soft layer of chemical products is assumed to be formed on top of the polished surface due to chemical reaction with a rate much faster than the MAR. It is then followed by a gentle mechanical abrasion of that soft layer. It is found that, for pure copper exposed to ammonium hydroxide, the yield strength of film is about 50% of the substrate yield strength; the modulus of film is about 20% of the substrate modulus. The film thickness is found to be in the order of few nanometers, and increases with the exposure time according to first order linear kinetics. Mechanism-II is based on mechanical abrasion accelerating CDR. In this case, the nano-wear experiment is first performed to generate local variation of the residual stress levels, and then followed by chemical exposure to investigate the variation of the wear depth and the evolution of surface topography. It is found that the residual stress caused by the mechanical wear enhances the CDR, as manifested by the increase of wear depth. The developed understanding from these experiments can be used in future studies to control the relative rates of CDR and MAR as well as investigating the various process-induced defects.

Mechanics and Physics of Solids, Uncertainy, and the Archetype-Genome Exemplar

Greene, M. Steven Northwestern University 2012 해외박사(DDOD)

This dissertation argues that the mechanics and physics of solids rely on a fundamental exemplar: the apparent properties of a system depend on the building blocks that comprise it. Building blocks are referred to as archetypes and apparent system properties as the system genome. Three entities are of importance: the archetype properties, the conformation of archetypes, and the properties of interactions activated by that conformation. The combination of these entities into the system genome is called assembly. To show the utility of the archetype-genome exemplar, the dissertation presents the mathematical construction and computational implementation of a new theory for solid mechanics that is a continuum manifestation of the assembly process. The so-called archetype-blending continuum theory aligns the form of globally valid balance laws with physics evolving in a material's composite constitutive response so that, by rethinking conventional micromechanics, the theory accounts naturally for each piece of the genome assembly triplet: archetypes, interactions, and their conformation. With the pieces of the triplet isolated in the theory, materials genome design concepts that separately control microstructure and property may be gleaned from exploration of the constitutive parameter space. A suite of simulations that apply the new theory to polymer nanocomposite materials demonstrate the ability of the theory to predict a robust material genome that includes damping properties, modulus weakening, local strain amplification, and size effects. The dissertation also presents a theoretical assessment of the importance of uncertainty propagation in the archetype-genome exemplar. The findings from a set of computational experiments on instances of a general class of microstructured materials suggest that when overlap occurs between the size of the system geometry and the features of the conformation, material genomes become less certain. Increasing nonuniformity of boundary conditions and the size of random field correlation lengths exacerbate this conclusion. These criteria are combined into a scalar metric used to assess the impact of archetype-level uncertainties on the material genome for general scenarios in solid mechanics. Exemplary benchmark problems include bending in elastoplasticity and instability-induced pattern transition in porous elastomer. The contributions of this dissertation are threefold: (1) the mathematical construction of a new continuum theory for mechanics and physics of solids, (2) implementation of the theory, and (3) theoretical assessment of the scenarios in which material genomes deviate from determinism.