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Ning Wang's picture

Long-distance propagation of forces in a cell

What might be the differences, if there is any, between mechanical signaling and chemical signaling in a living cell?

Elastic model for proteins (polymers)

There has been a lot of attention on the study of mechanics of proteins and/or single molecules. Such study was typically implemented by using classical molecular dynamics (MD) simulation. In spite of ability to describe the dynamics of biological macromolecules (e.g. proteins), MD simulation exhibits the computational restriction in the spatial and temporal scale. In order to overcome such computational limitation, the coarse-grained model has recently been taken into account. In this review, I would take a look at a couple of coarse-grained models of protein molecules.

Meshfree Methods: Frequently Asked Questions

Questions about meshfree methods are now addressed in the forum, under the Computational Mechanics subheading.

If you click on a question below, you will be redirected to the forum. I will update this post as more questions are added. Other experts are encouraged to augment my response there.

1. If I have meshfree shape functions that satisfy Kronecker-Delta, can I satisfy essential boundary conditions?

2. Is a mesh required in meshfree methods?

1. If I have meshfree shape functions that satisfy Kronecker-Delta, can I satisfy essential boundary conditions?

Choose a channel featured in the header of iMechanica: 

In fact, this is a common misconception with meshfree methods. Shape functions that satisfy Kronecker-Delta take a value of one at the node, and vanish at every other node in the domain. Finite element shape functions, for example, are usually designed with this property. This makes the satisfaction of essential boundary conditions relatively simple: we just set or fix the degree of freedom at the node to what it should be on the boundary. Unfortunately, this is usually not sufficient to impose essential boundary conditions with meshfree methods.

The issue is that meshfree shape functions associated with nodes located on the interior of the domain do not typically vanish on the boundary. So, what happens between nodes is just as important as what happens at the nodes. An excellent paper discussing the various options for imposing essential boundary conditions with meshfree methods is provided by Fernandez-Mendez and Huerta, Computer Methods in Applied Mechanics and Engineering, 193, pp. 1257-1275, 2004. At present, Nitsche's method is accepted as being the most robust for essential boundary conditions with meshfree methods. It should also be noted that with Natural-Neighbor interpolants, this is not an issue and the boundary conditions can be imposed just like they are with finite elements.

Liu's picture

Void-induced strain localization at interfaces

We published this paper in APL on a study of the deformation near interfaces. It provides insight in the strain localization at the interface and its influence on the deformation in bulk metals. 

Abstract An optical full-field strain mapping technique has been used to provide direct evidence for the existence of a highly localized strain at the interface of stacked Nb/Nb bilayers during the compression tests loaded normal to the interface. No such strain localization is found in the bulk Nb away from the interface. The strain localization at the interfaces is due to a high void fraction resulting from the rough surfaces of Nb in contact, which prevents the extension of deformation bands in bulk Nb crossing the interface, while no distinguished feature from the stress-strain curve is detected.

Juil Yoon's picture

Why Do Freezing Rocks Break?

As you know, the volumetric expansion by 9% during the water-to-ice transition can generate tremendous pressure in a confined space is a common sense. As a result, one may expect freezing water to also fracture rocks.

However, in a recent article in Science, Bernard Hallet explains the power of the 9% water-to-ice expansion in confined spaces is undeniable, but it may rarely be significant for rocks under natural conditions, because it requires a tight orchestration of unusual conditions. Unless the rocks are essentially saturated with water and frozen from all sides, the expansion can simply be accommodated by the flow of water into empty pores, or out of the rock through its unfrozen side.

I think it may be of interest to mechanics. Read more
I hope to hear opinions from people who know about the breaking mechanics of rocks.

Joost Vlassak's picture

Plastic deformation of freestanding thin films: Experiments and modeling

This is a paper we recently published in JMPS on a study of the mechanical properties on thin films comparing experimental results with discrete dislocation simulations. It provides insight in the strengthening that occurs in thin metal films when surface or interface effects become important.

The abstract is below; the full paper can be downloaded from here

Abstract - Experimental measurements and computational results for the evolution of plastic deformation in freestanding thin films are compared. In the experiments, the stress–strain response of two sets of Cu films is determined in the plane-strain bulge test. One set of samples consists of electroplated Cu films, while the other set is sputter-deposited. Unpassivated films, films passivated on one side and films passivated on both sides are considered. The calculations are carried out within a two-dimensional plane strain framework with the dislocations modeled as line singularities in an isotropic elastic solid. The film is modeled by a unit cell consisting of eight grains, each of which has three slip systems. The film is initially free of dislocations which then nucleate from a specified distribution of Frank–Read sources. The grain boundaries and any film-passivation layer interfaces are taken to be impenetrable to dislocations. Both the experiments and the computations show: (i) a flow strength for the passivated films that is greater than for the unpassivated films and (ii) hysteresis and a Bauschinger effect that increases with increasing pre-strain for passivated films, while for unpassivated films hysteresis and a Bauschinger effect are small or absent. Furthermore, the experimental measurements and computational results for the 0.2% offset yield strength stress, and the evolution of hysteresis and of the Bauschinger effect are in good quantitative agreement.

Qing Ma's picture

MEMS Switch Reliability

It is well-recognized that MEMS switches, compared to their more traditional solid state counterparts, have several important advantages for wireless communications.  These include superior linearity, low insertion loss and high isolation.  Indeed, many potential applications have been investigated such as Tx/Rx antenna switching, frequency band selection, tunable matching networks for PA and antenna, tunable filters, and antenna reconfiguration. 

However, none of these applications have been materialized in high volume products to a large extent because of reliability concerns, particularly those related to the metal contacts.  The subject of the metal contact in a switch was studied extensively in the history of developing miniaturized switches, such as the reed switches for telecommunication applications.  While such studies are highly relevant, they do not address the issues encountered in the sub 100mN, low contact force regime in which most MEMS switches operate.  At such low forces, the contact resistance is extremely sensitive to even a trace amount of contamination on the contact surfaces.  Significant work was done to develop wafer cleaning processes and storage techniques for maintaining the cleanliness.  To preserve contact cleanliness over the switch service lifetime, several hermetic packaging technologies were developed and their effectiveness in protecting the contacts from contamination was examined.  

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: SOURCE IDENTIFICATION AND SIMULATION

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.

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