# MEAM Seminar Series Archive: Fall 2007

Francois Willot

"

**Strain localization and effective medium properties**

**in 2D perfectly-plastic porous materials: the 'dilute' limit**"

**Speaker: Francois Willot**

Postdoctoral Researcher

Mechanical Engineering and Applied Mechanics,
University of Pennsylvania

**Abstract: **

This work addresses a notoriously difficult problem of nonlinear behavior and infinite contrast between two phases, one of which is a plastic solid phase, and the other one the porosity of the medium. Such problem is of special interest to effective-medium approximations, which typically reach their limits in situations of strong nonlinearity and high contrast between the phases.

The aim of this study is to investigate how plastic strain localization manifests itself at the level of the overall effective behavior of the medium in presence of pores, and in particular in the non-trivial limit of small porosity. This question, important to the understanding of ductile damage, is examined both numerically and theoretically, in the special case of two dimensional systems, and with a deformation-theory approach of plasticity. The numerical investigations consist of quasi-exact computations of the stress and strain fields in the voided medium, by means of the Fast Fourier Transform method making use of a particular choice for Green's function. The theoretical approach makes use of exact solutions, which can be obtained in particular cases of a periodic void lattice, as well as of a recent "second-order" nonlinear homogenization approach. The virtues of the latter are evaluated in two steps, first by studying the underlying linear anisotropic homogenization step (an essential ingredient), then by studying the nonlinear step itself. A connection between the strain/stress localization patterns and the macroscopic behavior is shown in the case of a strongly anisotropic linear material. In the nonlinear case, the nature and significance of the singularities, confirmed by FFT computations, are partly elucidated.

Safety Seminar

**Speakers: ****Joe Passante, CIH **

Sr. Industrial Hygienist Environmental Health & Radiation Safety

**Karen Kelley, CIH**

Industrial Hygienist, Laser Safety Officer

**Terry Kientz**

Electronic Engineer

**Melissa Muth**

Sr. Information Security Specialist

**Topics Covered**: Computer Security and Copyrights, General Lab Safety, Laser Safety, and Additional Lab Issues

***All first year MEAM graduate students must attend.**

Kostas Danas, PhD Candidate

"

**Homogenization-based constitutive models for viscoplastic porous media with evolving microstructure**"

**Speaker: Kostas Danas**

PhD Candidate

Adviser: **Pedro Ponte Castañeda**

Mechanical Engineering and Applied Mechanics,
University of Pennsylvania

**Abstract: **

This work is concerned with the application of the "second-order" nonlinear homogenization procedure of Ponte Castañeda (2002) to generate estimates of the Willis (1977) type for the effective behavior of viscoplastic porous materials. The main concept behind this procedure is the construction of suitable variational principles utilizing the idea of a "linear comparison composite" to generate corresponding estimates for the nonlinear porous media. Thus, the main objective of this work is to propose a general constitutive model that accounts for the evolution of the microstructure and hence the induced anisotropy resulting when the porous material is subjected to finite deformations.

The model is constructed in such a way that it reproduces exactly the behavior of a "composite-sphere" assemblage in the limit of hydrostatic loadings, and therefore coincides with the hydrostatic limit of Gurson's (1977) criterion in the special case of ideal plasticity and isotropic microstructures. As a consequence, the new model improves on earlier homogenization estimates, which have been found to be quite accurate for low triaxialities but overly stiff for sufficiently high triaxialities and nonlinearities. Additionally, the estimates delivered by the model exhibit a dependence on the third invariant of the macroscopic stress tensor, which has a significant effect on the effective response of the material at moderate and high stress triaxialities.

Finally, the above-mentioned results are generalized to more complex anisotropic microstructures (arbitrary pore shapes and orientation) and general, three-dimensional loadings, leading to overall anisotropic response for the porous material. The model is then extended to account for the evolution of microstructure when the material is subjected to finite deformations. To validate the proposed model, finite element axisymmetric unit-cell calculations are performed and the agreement is found to be very good in all the range of stress triaxialities and nonlinearities considered.

Doyoung Byun

"

**Development of electrostatic field induced inkjet head: Microscale and nanoscale patterning"**

**Speaker: Doyoung Byun**

Visiting Assistant Professor, Mechanical Engineering and Applied Mechanics

University of Pennsylvania

(Konkuk University, Seoul, Korea)

**Abstract: **

This study presents a novel mechanism for an electrostatic field induced drop-on-demand ink-jetting device. Currently, the primary commercial implementation of inkjet technology is in the field of inkjet image printing. Recently, there has been a tremendous increase in the use of micro droplets in physical, chemical, biological, and engineering research areas. Performance factors such as high frequency jetting, high density of nozzle arrays, size of droplet, and uniformity of droplet size are required to fulfill the requirements of various applications. The conventional jetting devices based on thermal bubble or piezoelectric pumping, however, have some fundamental limitations to overcome in order to meet the aforementioned requirements for the future generation of jetting devices: 1) Thermal bubble jetting has fundamentally limitation in size and density of the nozzle array as well as the ejection frequency, mainly due to thermal problems. 2) Mechanical jetting, such as in piezoelectric devices, has limits in the density of the nozzle array, the ejection frequency limited by physical properties, and the reliability limited due to the difficulty of fabrication.

Electrostatic jetting of liquids is a physical process caused by an electric force applied to the surface of a liquid. The electrical shear stress elongates the liquid meniscus formed at the opening of the nozzle and generates a tiny droplet as a result of the balance between electrical and surface tension forces. The electric voltage signal applied allows for a strong electric field to be concentrated in the vicinity of the apex of the liquid meniscus and thus micro-dripping ejection of droplet takes place. That is, a tiny droplet is removed from the peak of the dome-shaped liquid meniscus. Optimal conditions are introduced for applied voltage, electric conductivity, and flow rate for generating a stable drop-on-demand droplet using the micro-dripping mode. It is also verified experimentally that the use of the pole-type nozzle allows a stable and sustainable micro-dripping mode of droplet ejection for a wide range of applied voltages, demonstrating the feasibility of an electrostatic field induced drop-on-demand ink-jetting device as an alternative to conventional inkjet print heads.

Also the theory is presented for jetting the distilled water and water with sodium dodecyl surfate (SDS). It has been observed that the droplet size decreases and the frequency of the droplet formation and the velocity of the droplet ejection increase with increasing the intensity of the electrostatic field. The results of the experiments have shown good agreement with those of numerical analysis.

In general, the limitations of inkjet technology have precluded printing patterns smaller than 20 um, and it seems that, despite the large pressure on low-cost manufacturing, the wide application was not opened yet. On the other hand, since, in 1993, Kumar discovered that a polymer inked with an alkanethiol can form a monolayer on a gold surface, microcontact printing has given rise to the development of soft lithography. It is reported that currently the smallest size moldable with high aspect ratio is 50 nm. Even if nanoscale high accuracy is achievable with soft lithography, alignment issues and low printing speed remain challenges. Between microscale printing approaches and nanoscale soft-lithography approaches, there is a big gap from 20 um and around 50 nm. There is a genuine need for nano-to-macro integration. Therefore, innovations are needed to drive printing technologies to reduce pattern sizes from 20 um to 50 nm. In this ongoing study, preliminary results are introduced to enable the patterning of nanoscale elements and structures and facilitating microscale and nanoscale structures' integration.

Johsua W. Lampe, PhD Candidate

"

**Interfacial characteristics of a gas bubble immersed in a surfactant and protein lade fluid: Experimentation and modeling**"

**Speaker: Johsua W. Lampe**

PhD Candidate

Advisor: **P.S. Ayyaswamy**

Mechanical Engineering and Applied Mechanics,
University of Pennsylvania

**Abstract: **

This dissertation is a study of macromolecule adsorption to a gas-liquid interface. This study is of broad interest to such diverse fields as material science, food science, cardiology, and polymer science. All of these fields involve interfacial phenomena of the type investigated here. In this undertaking, surface tension measurements of single protein solutions, single tri-block copolymer solutions, binary protein solutions, and protein tri-block copolymer solutions have been recorded as a function of time and bulk concentration. A model for the equilibrium surface tension of a single protein solution based on 3-D dense packing has been provided herein. The tri-block copolymer equilibrium surface tension behavior is accurately modeled by the Langmuir Isotherm in dilute concentrations. The equilibrium surface tension behavior of surfactant-protein and protein-protein mixtures has also been modeled. Here, competition has been found to be comprised of two types, steric competition and energetic competition. This new competitive model accurately captures previously unreported effects related to competitive adsorption, especially cooperative surface tension change at low bulk concentrations.

In addition to surface tension measurements, a novel Laser Scanning Confocal Microscopy method is described for the measurement of the adsorbed surface excess concentration. Modeling of protein adsorption has been, in general, confounded by the inability to accurately measure the surface excess at the gas liquid interface. The method described in this dissertation involves the imaging of fluorescently labeled protein molecules in a droplet placed on a microscope cover slip, and holds great promise. It is especially suited to measuring the surface excess of a small number of competing protein or surfactant species.

David G. Cahill

"

**Extremes in heat conduction:**

**Pushing the boundaries of the thermal conductivity of materials"**

**Speaker: David G. Cahill**

Department of Materials Science and Engineering

Frederick Seitz Materials Research Laboratory

University of Illinois

**Abstract: **

Thermal conductivity is a basic and familiar property of materials: silver spoons conduct heat well and plastic does not. In recent years, an interdisciplinary group of materials scientists, engineers, physicists, and chemists have succeeded in pushing-back long-established limits in the thermal conductivity of materials. The current champion at the high end of the thermal conductivity spectrum is carbon nanotubes, due to their high sound velocities and relative lack of processes that scatter phonons. Unfortunately, the superlative thermal properties of nanotubes have not found immediate application because of difficulties in making good thermal contact with nanotubes, i.e., the thermal conductance of interfaces with nanotubes is very small. At the low end of the thermal conductivity spectrum, solids that combine order and disorder in the random stacking of two-dimensional crystalline sheets, so-called “disordered layered crystals” show a thermal conductivity that is only a factor of 2 larger than air; the cause of this low thermal conductivity is not fully understood but may be explained by a large fraction of vibrational modes that are localized and neither propagate as waves (as in crystals) or transport diffusively (as in glasses).

William Schultz

"

**Viscoelastic effects in glass fiber spinning**"

**Speaker: William Schultz**

Director, Fluid Dynamics Program, National Science Foundation

Professor of Mechanical Engineering and Applied Mechanics,
University of Michigan

**Abstract:
**We show that viscoelastic effects are required to understand draw resonance inhibition and the attainment of high ultimate tensile strength in glass fibers. The process is shown to not be thermo-rheologically simple. A rheological model is presented that shows some promise in modeling the fiber spinning process.

At the end, funding trends and solicitations at NSF will be discussed, especially in the areas of fluid mechanics.

Dimos Poulikakos

"

**Thermofluidics with nanoparticles and carbon nanotubes: On their physics and related novel technologies**"

**Speaker: Dimos Poulikakos**

Professor and Director, Laboratory of Thermodynamics in Emerging Technologies, Institute of Energy Technology, ETH

Zurich, Switzerland

**Abstract: **

In this lecture, the topic of nanoparticles in thermofluidics will be addressed. The focus will be carbon nanotubes, with many unique properties and gold nanoparticles, which possess significantly lower melting temperatures compared to the melting temperature of bulk gold. Using molecular dynamics simulations, we demonstrate and quantify thermophoretic motion of solid gold nanoparticles inside carbon nanotubes subject to wall temperature gradients ranging from 0.4 to 25 K/nm. The particles move “on tracks” in a predictable fashion as they follow unique helical orbits depending on the geometry of the carbon nanotubes. The observed thermophoretic motion correlates with the phonon dispersion exhibited by a standard carbon nanotube and, in particular, with the breathing mode of the tube. An increased static friction for gold nanoparticles confined inside a zig-zag carbon nanotube when increasing the length of the nanoparticles is found. An unexpected, opposite trend is observed for the same nanoparticles inside armchair tubes. The issue of functionalization of solid liquid interfaces to facilitate phonon transport and increase the interfacial thermal conductance will also be addressed. On the experimental front, the measurement of the thermal conductivity of individual multiwalled carbon nanotubes with a novel four-point-probe third-harmonic method will be discussed. A microfabricated device composed of four metal electrodes was modified to manufacture nanometer-sized wires by using a focused ion beam source. A carbon nanotube could then be suspended over a deep trench milled by the focused ion beam, preventing heat loss to the substrate. The multiwalled carbon nanotube was modelled as a one-dimensional diffusive energy transporter and its thermal conductivity was measured at room temperature under vacuum to be 300 ± 20 W/mK.

Moving on to gold nanoparticles, a novel process of direct writing and low temperature annealing of electrical conductors with nanoparticle inks on sensitive organic substrates will be presented and the complex multiscale and multiphase physics of the underlying processes will be discussed. Combining nanoparticles and nanotubes, a flexible polymer field effect transistor (FET) with a nanoscale (40 nm) carbon nanotube channel was conceptualized and realized. The device was manufactured by direct-writing and spincoating of polymers and gold nanoink. Carbon nanotubes were dispersed on a polyimide substrate and then marked in an SEM-FIB apparatus such that they could be contacted with gold nanoink. The CNTs were divided into two by a focused ion beam such that they can form the source and drain of the transistor. Poly(3-hexylthiophene)(P3HT) was direct written as an active layer. After fabrication the flexible transistors can be simply peeled off the substrate.

Nikolaos Aravas

"Constitutive modeling and finite element methods for trip steels"

**Speaker: Nikolaos Aravas**

Professor, Department of Mechanical and Industrial Engineering

University of Thessaly, GREECE

**Abstract: **

A constitutive model that describes the mechanical behavior of steels exhibiting “Transformation Induced Plasticity” (TRIP) during martensitic transformation is presented. Multiphase TRIP steels are considered as composite materials with a ferritic matrix containing bainite and retained austenite, which gradually transforms into martensite. The effective properties and overall behavior of TRIP steels are determined by using homogenization techniques for non-linear composites. A methodology for the numerical integration of the resulting elastoplastic constitutive equations in the context of the finite element method is developed and the constitutive model is implemented in a general-purpose finite element program. The model is calibrated by using experimental data of uniaxial tension tests in TRIP steels. The problem of necking of a bar in uniaxial tension is studied in detail. The constitutive model is used also for the calculation of “forming limit diagrams” for sheets made of TRIP steels; it is found that the TRIP phenomenon increases the strain at which local necking results from a gradual localization of the strains at an initial thickness imperfection in the sheet.

W. Gregory Sawyer

"

**Thermally activated friction**"

**Speaker: W. Gregory Sawyer**

Professor, Mechanical & Aerospace Engineering

University of Florida

**Abstract: **

There are a number of applications where operation in a temperature range from 200 to 400 K or larger is required for device success. These extreme conditions are often the motivation for variable temperature studies in tribology, but there is a paucity of relevant tribology data available for temperatures below 273 K. In the range from 300 K to 400 K the friction coefficient of various solid lubricants is shown to increase with decreasing temperature. It is well known that many solid lubricant films transfer and adhere strongly to the counterface, and a modern hypothesis is that both friction and wear of these films are dominated by the interactions of interfacial sliding at weak self-mated interfaces. Recent work by our group found that friction of polytetrafluoroethylene matrix composites continued to increase in the cryogenic regime down to 200 K, and the notion of a thermally activated friction coefficient was proposed (analysis of an activation energy gave Ea=3.7 kJ/mol). A recent molecular scale study of graphite used an atomic force microscope to collect friction data on molecularly smooth terraces of over a temperature range from 140 K to 750 K at a vacuum level of 2x10-10 torr. The friction coefficient again increased with decreasing temperature, and the data collected followed an Arrhenius dependence with an activation energy of Ea = 9.6 kJ/mol. These molecular scale experiments addressed many of the uncertainties raised in the macroscopic experiments conducted by our group; namely, the sliding interface was well characterized, interfacial sliding was confirmed, and the experiments were run in ultra-high-vacuum at temperatures well above the temperature for equilibrium ice formation on the surfaces (*frost-point*).

Shravan Veerapaneni, PhD Candidate

"

**High-order fast integral equation methods for PDEs with moving interfaces"**

**Speaker: Shravan Veerapaneni**

PhD Candidate

Advisor:**George Biros**

Department of Mechanical Engineering and Applied Mechanics

University of Pennsylvania

**Abstract: **

Vesicles are locally-inextensible closed membranes that possess tension and bending energies. Vesicle flows model numerous biophysical phenomena that involve deforming particles interacting with a Stokesian fluid. For instance, they are used to model red blood cell motion and the transport of drug-carrying capsules. While conventional techniques can be used to simulate isolated vesicles, new approaches are needed for large number of interacting vesicles. Integral equation methods are attractive for these problems as they avoid the need for volume mesh generation and re-meshing. They lead to a system of nonlinear integro-differential equations whose unknowns reside on the fluid-vesicle interfaces. We have developed a novel numerical scheme for such equations. The scheme is high-order accurate and achieves optimal algorithmic complexity. It incorporates a new time-stepping scheme that allows much larger time-steps than the existing explicit schemes. The associated linear systems are solved in optimal time using spectral preconditioners, FFTs and the fast multipole method. We present numerical results that demonstrate the effectiveness of our scheme.

Eliot Fried

"A conjectured hierarchy of length scales in a generalization of the Navier–Stokes-α equation for turbulent fluid flow"

**Speaker: Eliot Fried**

Professor, Department of Mechanical and Aerospace Engineering

Washington University

**Abstract: **

We present a continuum-mechanical formulation and generalization of the Navier–Stokes-α theory based on a general framework for fluid-dynamical theories with gradient dependencies. Our flow equation involves two additional problem-dependent length scales α and β. The first of these scales enters the theory through the internal kinetic energy, per unit mass, α^{2} |D|^{2}, where D is the symmetric part of the gradient of the filtered velocity. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity. When α and β are equal, our flow equation reduces to the Navier–Stokes-α equation. In contrast to the original derivation of the Navier–Stokes-α equation, which relies on Lagrangian averaging, our formulation delivers boundary conditions. For a confined flow, our boundary conditions involve an additional length scale l characteristic of the eddies found near walls. Based on a comparison with direct numerical simulations for fully-developed turbulent flow in a rectangular channel of height 2*h*, we find that α/ β~Re^{0.470} , where Re is the Reynolds number. The first result, which arises as a consequence of identifying the internal kinetic energy with the turbulent kinetic energy, indicates that the choice α=β required to reduce our flow equation to the Navier–Stokes-α equation is likely to be problematic. The second result evinces the classical scaling relation η/*L*~Re^{-3/4} for the ratio of the Kolmogorov microscale η to the integral length scale *L*. The numerical data also suggests that l≤β. We are therefore led to conjecture a tentative hierarchy, l≤β<α, involving the three length scales entering our theory.

N. Sukumar

"Partition of unity finite elements for electronic-structure calculations in molecules and crystalline solids"

**Speaker: N. Sukumar**

Associate Professor,
Department of Civil and Environmental Engineering

University of California, Davis

**Abstract: **

Over the past few decades, the planewave pseudopotential (PW) method has established itself as the method of choice for large, accurate quantum-mechanical calculations in solids and liquids. However, due to its global Fourier basis, the PW method suffers from substantial inefficiencies in parallel implementation and in problems involving localized states. Modern real-space methods such as finite-differences (FD), finite elements (FE), and wavelets, resolve these problems but have until now required a much larger number of basis functions to attain the required accuracy. In this talk, I will present a new real-space finite element method to solve the Kohn-Sham equations of density functional theory. We employ partition-of-unity (PU) enrichment techniques to build the known atomic physics into the FE basis, thereby substantially reducing the degrees of freedom required. The unit cell is parallelepiped, and we consider Dirichlet boundary conditions for atoms and molecules, and Bloch-periodic boundary conditions for crystalline solids. A new approach to impose Bloch-periodic boundary conditions (arbitrary *k*-points) in FE and PUFE methods is also developed. Structured meshes consisting of higher-order `serendipity’ finite elements (8-, 20-, and 32-node brick elements) are used to construct the FE basis, and trilinear finite elements are used to form the PU basis. The enrichment functions are pseudoatomic wavefunctions ψ* _{nlm}*(

**x**)=

*R*

*(*

_{nl}*r*)

*Y*

*(θ,φ), the product of radial solutions and spherical harmonics. A one-dimensional spectral finite element solver is used to compute*

_{lm}*R*

*(*

_{nl}*r*). Our initial results for the energy eigenvalues show order-of-magnitude improvements relative to current state-of-the-art PW and adaptive-mesh (AMR) FE methods for systems involving localized states such as d- and f-electron systems.