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Mogadalai Gururajan's picture

Microstructural evolution in elastically inhomogeneous systems

I am very happy to be part of iMechanica, and what best way to start than post some stuff that I have been doing recently. I received my PhD for a thesis I submitted to the Department of Materials Engineering (formerly Department of Metallurgy), Indian Institute of Science, Bangalore 560012 INDIA titled Elastic Inhomgeneity Effects on microstructures: a phase field study.

A mismatch in elastic moduli is the primary driving force for certain microstructural changes; for example, such a mismatch can result in rafting, phase inversion, and thin film instability.

My thesis is based on a phase field model, which is developed for the study of microstructural evolution in elastically inhomogeneous systems which evolve under prescribed traction boundary conditions; however, we show that it is also capable of simulating systems which are evolving under prescribed displacements.

The (iterative) Fourier based methodology that we adopt for the solution of the equation of mechanical equilibrium is characterised by comparing our numerical elastic solutions with corresponding analytical sharp interface results; in addition to being accurate, this solution methodology is also very efficient. We integrate this solution methodology into our phase field model, to study microstructural evolution in systems with dilatational misfit.

Zhigang Suo's picture

Mechanics of climbing and attachment in twining plants

In a recent article in Physical Review Letters, Alain Goriely and Sébastien Neukirch offer a mechanical model of how the free tip of a twining plant can hold onto a smooth support, allowing the plant to grow upward. The model also explains why these vines cannot grow on supports of too large a diameter. Read more.

The mechanics involves large deflection and bifurcation of a rod. I hope to hear opinions from people who know about the mechanics of plants.

MichelleLOyen's picture

Variability in Bone Indentation

A viscous-elastic-plastic indentation model was used to assess the local variability of properties in healing porcine bone. Constant loading- and unloading-rate depth-sensing indentation tests were performed and properties were computed from nonlinear curve-fits of the unloading displacement-time data. Three properties were obtained from the fit: modulus (the coefficient of an elastic reversible process), hardness (the coefficient of a nonreversible, time-independent process) and viscosity (the coefficient of a nonreversible, time-dependent process). The region adjacent to the dental implant interface demonstrated a slightly depressed elastic modulus along with an increase in local time-dependence (lower viscosity); there was no clear trend in bone hardness with respect to the implant interface.

Wei Hong's picture

Dynamics of terraces on a silicon surface due to the combined action of strain and electric current

A (001) surface of silicon consists of terraces of two variants, which have an identical atomic structure, except for a 90° rotation. We formulate a model to evolve the terraces under the combined action of electric current and applied strain. The electric current motivates adatoms to diffuse by a wind force, while the applied strain motivates adatoms to diffuse by changing the concentration of adatoms in equilibrium with each step. To promote one variant of terraces over the other, the wind force acts on the anisotropy in diffusivity, and the applied strain acts on the anisotropy in surface stress. Our model reproduces experimental observations of stationary states, in which the relative width of the two variants becomes independent of time. Our model also predicts a new instability, in which a small change in experimental variables (e.g., the applied strain and the electric current) may cause a large change in the relative width of the two variants.

Jie Wang's picture

On the solution to time-dependent Ginzburg-Laudau (TDGL) equation

Time-dependent Ginzburg-Laudau (TDGL) equation is the simplest kinetic equation for the temporal evolution of a continuum field, which assumes that the rate of evolution of the field is linearly proportional to the thermodynamical driving force. The computation model based on this equation is also called phase field model. Phase field simulation can predict quite beautiful patterns of microstructures of material. It has been widely applied to simulating the evolution of microstructure by choosing different field variables. For example, using the single conserved field (concentration field), continuum phase field models has been employed to describe the pattern formation in phase-separating alloys (Nishimori and Onuki, 1990 Phys. Rev. B, 42,980) and the nanoscale pattern formation of an epitaxial monolayer (Lu and Suo, 2001 J. Mech. Phys. Solids, 49,1937). On the other hand, using the nonconserved field (polarization field), the phase field model has been utilized to simulating the formation of domain structure in ferroelectrics (Li et al. 2002  Acta Mater, 50,395). The thermodynamical driving force is usually nonlinear with respect to the field variable. In the case of nonlinearity, the solution to TDGL equation may not be unique. Different grid density, length of iteration step, initial state and random term (introduced to describe the nucleation process) may induce different results in the simulation. Does anyone investigate the effect of these factors on the final pattern? I wonder whether we can prove the solution is unique or not.       

Xi Wang's picture

Laser Annealing of Amorphous NiTi Shape Memory Alloy Thin Films to Locally Induce Shape Memory Properties

Xi Wang, Yves Bellouard, Joost J. Vlassak

Published in Acta Materialia 53 (2005) p4955-4961.

Abstract — We present the results of a crystallization study on NiTi shape memory thin films in which amorphous films are annealed by a scanning laser. This technique has the advantage that shape memory properties can be spatially distributed as required by the application. A kinetics study shows that nucleation of the crystalline phase occurs homogenously in the films. Consequently, the laser annealing process produces polycrystalline films with a random crystallographic texture. The crystallized films have a uniform microstructure across the annealed areas. The material in the crystalline regions transforms reversibly to martensite on cooling from elevated temperature and stress measurements show that a significant recovery stress is achieved in the films upon transformation.

Xi Wang's picture

Cross-section TEM micrograph of a NiTi crystal in a partially crystallized film

This micrograph indicates the nulceation and growth mechanism in the crystallization of amorphous near-equiatomic NiTi films. The crystal nucleates homogenously inside the bulk of the film, and quickly consume most of the film thickness, and then grows laterally in a two-dimensional growth mode. Heterogeneous nucleation at an interface was not observed due to the composition shift at those locations caused by interfacial reaction.

Nanoscale Intracellular Organization and Functional Architecture Mediating Cellular Behavior

Cells function based on a complex set of interactions that control pathways resulting in ultimate cell fates including proliferation, differentiation, and apoptosis. The interworkings of his immensely dense network of intracellular molecules are influenced by more than random protein and nucleic acid distribution where their interactions culminate in distinct cellular function.

Xiao Hu Liu's picture

Pattern Effect on Low-k Channel Cracking

Low dielectric constant (low-k) is achieved often at the cost of degraded mechanical properties, making it difficult to integrate the dielectric in the back end of line (BEOL) and to package low-k chips. Development of low-k technology becomes costly and time-consuming. Therefore, more frequently than before, people resort to modeling to understand mechanical issues and avoid failures. In this paper we present three multilevel patterned film models to examine channel cracking in low-k BEOL. The effects of copper features, caps and multilevel interconnects are investigated and their implications to BEOL fabrication are discussed.

Low-k BEOL Mechanical Modeling
Liu, Xiao Hu; Lane, Michael W; Shaw, Thomas M; Liniger, Eric G; Rosenberg, Robert R; Edelstein, Daniel C
Advanced Metallization Conference 2004 (AMC 2004); San Diego, CA and Tokyo; USa and Japan; 19-21 Oct. 2004 and 28-29 Sept. 2004. pp. 361-367. 2005

Yanfei Gao's picture

Nanoscale incipient asperity sliding and interface micro-slip assessed by the measurement of tangential contact stiffness

Experiments with a multidimensional nano-contact system (Lucas, Hay, and Oliver, J. Mater. Res. 2004) have shown that, prior to kinetic frictional sliding, there is a significant reduction of the tangential contact stiffness relative to the elastic prediction. The reduction occurs at contact sizes below about 50~200nm for aluminum single crystals and several other materials. Using a cohesive interface model, we find that this reduction corresponds to a transition from a small-scale-slip to large-scale-slip condition of the interface.

Jie Wang's picture

The effect of long-range elastic interactions on the toroidal moment of polarization in a ferroelectric nanoparticle

The effect of long-range (LR) elastic interactions on the toroidal moment of polarization in a two-dimensional ferroelectric particle is investigated using a phase field model. The phase field simulations exhibit vortex patterns with purely toroidal moments of polarization and negligible macroscopic polarization when the spontaneous strains are low and the simulated ferroelectric size is small. However, a monodomain structure with a zero toroidal moment of polarization is formed when the spontaneous strains are high in small simulated ferroelectrics, indicating that, because of the LR elastic interactions, high values of spontaneous strains hinder the formation of polarization vortices in ferroelectric particles. Applied Physics Letters 88, 182904 (2006)

Rui Huang's picture

New Hot Paper Comment by George M. Pharr

I came across this page and think it may be of interest to mechanicians.

Ravi-Chandar's picture

A blog for the International Journal of Fracture

I am pleased to announce that a new blolg associated with the International Journal of Fracture has been created by Springer. This is an ambitious project that aims to augment the published version of the papers and to create a dialogue between authors and readers. All articles beginning with the Dec 2004 issue now have a blog entry; ealier volumes will be added as digital processing of information continues. Discussion is not restricted to papers published in the journal, but should relate to the fracture/failure/structural integrity theme/micromechanics. Please see my post of Oct 25, 2006 for a detailed description of the obectives of the blog. I welcome your particpation in this experiment to enhance archival publication.

Min Huang's picture

The Influence of Light Propagation Direction on the Stress-Induced Polarization Dependence in Si Waveguides

The effects of light propagation direction on the stress induced polarization dependence of silicon-based waveguide were studied. As silicon is an anisotropic material, the change of polarization dependence induced by the photoelastic effect depends on the light propagation directions. It is found that when the light propagates in <100> directions on {100} silicon, the changes of refractive index and polarization shift are about 20% more sensitive to the stress than those when the light propagates in <110> directions. (IEEE Photonic Technology Letters, vol.

Pradeep Sharma's picture

Nonlinear Stability Analysis of Self-assembling Nanoscale Patterns

I thought I should take advantage of iMechanica and obtain feedback on some recent work that we did on nonlinear stability analysis of patterns.

A paradigmatic model that governs monolayer self-assembly was constructed a few years back by Wei Lu (Michigan) and Zhigang Suo. Apart from obtaining several physical insights they also conducted a linear stability analysis of their model. Borrowing technqiues from the nonlinear physics community, our work presents nonlinear stability analysis i.e. the initial state is no longer homogeneous and stable states beyond the transition are calculated. This allows a detailed construction of stability maps for various patterns without extensive numerical calculations.

This work is currently under review and I am attaching a pre-print with this post. Any comments and suggestions would be well-appreciated.

Wei Hong's picture

Persistent step-flow growth of strained films on vicinal substrates

We propose a model of persistent step flow, emphasizing dominant kinetic processes and strain effects. Within this model, we construct a morphological phase diagram, delineating a regime of step flow from regimes of step bunching and island formation. In particular, we predict the existence of concurrent step bunching and island formation, a new growth mode that competes with step flow for phase space, and show that the deposition flux and temperature must be chosen within a window in order to achieve persistent step flow. The model rationalizes the diverse growth modes observed in pulsed laser deposition of SrRuO3 on SrTiO3

 Physical Review Letters 95, 095501 (2005)

zishun liu's picture


Snoring is defined as sounds made by vibrations in the soft palate and their adjacent tissues during sleep. Heavy snoring can result in sleep-related upper airway narrowing, which leads to respiratory flow limitation and increased respiratory effort. If untreated, heavy snoring may be complicated by excessive daytime sleepiness. Hence, snoring has received a great deal of clinical attention in recent years.

fengliu's picture

Nanomechanical Architecture of Strained Bi-layer Thin Films:from design principles to experimental fabrication

The nanotechnology of the future demands controlled fabrication of nanostructures. Much success has been made in the last decade in fabricating nanostructures on surface with desirable size and shape, either in serial using scanned-probe techniques or in parallel using self-assembly/self-organization processes sometimes combined with lithographic patterning techniques. However, controlled fabrication of nanostructures remains in general a formidable challenge. For example, despite the enormous success we have so far enjoyed with carbon nanotubes (CNTs), it is still very difficult (if not impossible) to synthesize CNTs with a degree of control that we would like in terms of their size and chirality. Fabrication of nanostructures in many other forms and with other materials is even less developed. There exists a strong need for the development of nanofabrication techniques with higher degree of control. Here, we demonstrate the general design principles of an emerging nanofabrication approach based on nanomechanical architecture of strained bi-layer thin films, which allows fabrication of a variety of nanostructures, such as nanotubes, nanorings, nanodrills, and nanocoils, with an unprecedented level of control.

Konstantin Volokh's picture

Prediction of femoral head collapse in osteonecrosis

OSTEONECROSIS is the death of bone that results in the collapse of the bony structure, leading to joint pain, bone destruction, and loss of function. Destruction of the bone frequently is severe enough to require joint replacement surgery. Osteonecrosis is a common disorder and accounts for 10% or more of the 500,000 total joint replacement procedures performed annually in the United States. Approximately 75% of patients with osteonecrosis are between 30 and 60 years of age.

From the point of view of mechanics, osteonecrosis means deterioration of mechanical properties of the bone. Decrease of the magnitude of the elastic modulus of the bone leads to its inability to bear the external load and culminates in bone damage and fracturing. For a couple of decades the engineers were trying to estimate the critical stress-strain state of the femoral head using the available data on the osteonecrotic bone properties, finite element analysis based on 3D elasticity, and Von Mises stress as a criticality condition. The fact that the cortical shell of the femoral head is significantly stiffer than the underlying cancellous bone did not attract much attention yet. However, from the solid mechanics point of view the difference in the stiffness of the cortical and cancellous parts of the femoral head under both normal and necrotic conditions is important. This difference allows for considering the femoral head as an elastic cortical shell on an elastic cancellous foundation. This, in its turn, suggests the buckling of the cortical shell as a possible starting point of the overall head collapse. The purpose of the study, described here, was to assess the cortical shell buckling scenario as a possible mechanism of the femoral head collapse at the various stages of osteonecrosis.

Dhirendra Kubair's picture

Finite element simulations of microvoid growth due to selective oxidation in binary alloys.

Selective oxidation induced void growth is observed in thermal barrier coating (TBC) systems used in gas turbines. These voids occur at the interface between the bond coat and the thermally grown oxide layer. In this article we develop the modeling framework to simulate microvoid growth due to coupled diffusion and creeping in binary alloys. We have implemented the modeling framework into an existing finite element program. The developed modeling framework and program is used to simulate microvoid growth driven by selective oxidation in a binary beta-NiAl alloy. Axisymmetric void growth due to the combined action of interdiffusion and creeping is simulated. The sharpness of the void and direction of creeping are considered as parameters in our study. Our simulations show that the voids dilate without any change in shape when creeping is equally likely in all the directions (isotropic). Void growth patterns similar to those observed in experiments are predicted when the creeping is restricted to occur only along the radial and tangential directions. A hemispherical void grows faster compared to a sharp void. The sharpness increases in the case of a sharp void and could lead to interactions with the neighboring voids leading to spallation of the thermally grown oxide layer as observed in experiments.

Xi Chen's picture

Mystical materials in indentation

As an indenter penetrates an elastoplastic material, the indentation load P can be measured as a continuous function of the indentation displacement δ, to obtain the so-called P-δ curve. A primary goal of the indentation analysis is to relate the material elastoplastic properties (such as the Young's modulus, yield stress, and work-hardening exponent) with the indentation response (i.e. the shape factors of the P-δ curve, including its curvature, unloading stiffness, loading work, unloading work, maximum penetration, residual penetration, maximum load, etc.). The sharp indenters (e.g.

Dynamics of wrinkle growth and coarsening in stressed thin films

Rui Huang and Se Hyuk Im, Physical Review E 74, 026214 (2006).

A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a simple scaling law under uniaxial compression. Slightly different dynamics is observed under equi-biaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a labyrinth pattern under equi-biaxial stresses. Both have the same wavelength, independent of the initial stress. On the other hand, the wrinkle amplitude depends on the initial stress state, which is higher under an equi-biaxial stress than that under a uniaxial stress of the same magnitude.

Ju Li's picture

Localization Lengthscale in Metallic Glass

See an accompanying powerpoint presentation: The aged-rejuvenation-glue-liquid (ARGL) shear band model has been proposed for bulk metallic glasses (Acta Mater. 54 (2006) 4293), based on small-scale molecular dynamics simulations and thermomechanical analysis. The model predicts the existence of a critical lengthscale ~100 nm and timescale ~100 ps, above which melting occurs in shear-alienated glass. Large-scale molecular dynamics simulations with up to 5 million atoms have directly verified these predictions. When the applied stress exceeds the glue traction (computed separately before), we indeed observe maturation of the shear band embryo into bona fide shear crack, accompanied by melting.

A message from Dr. Ken P. Chong

The deadline of October 1, 2006 for my program of Mechanics & Structures of Materials was inadvertently omitted in our website. However, at the beginning of our CMS home page there are 2 deadlines listed for all programs. In the meantime any unsolicited proposals for my program, please put in GPG 04-23 as the Program Announcement [1st box]. In the 2nd box put in my program name [Mechanics & Structures of Materials].


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