Mechanics and Materials Engineering

A large variety of biological movements occur in a fluid environment. In this talk, we present a number of such biological problems where fluid motion on small scales plays an important role. We first discuss the motion on a single cell, the bacterium E. coli, and show how hydrodynamic interactions with a nearby surface can lead to circular swimming motion. We then consider cell locomotion in viscoelastic fluids, as is relevant in reproduction and spermatozoa swimming, and show how non-Newtonian stresses can provide biological advantages. Thirdly, we discuss the mechanics of snail locomotion, and show how the mechanical properties of the (thin) snail mucus can be tuned to decrease the cost of locomotion. We finish by a quick overview of other topics of current research.

“Fluidic Miniaturization – Siognificance, Techniques, Devices, and Applications”

Currently, molecular biology and biomedical science are under intensifying pressure to address increasingly hard problems that create a strong demand for inexpensive, sophisticated, high-throughput, organizationally simple, decentralized solutions. It is exactly such solutions that the new technology of elastomer microfluidics offers to provide by means of its unparalleled capability for complex fluidic control and function at the microscale.

The present talk first introduces basic microfluidic techniques and devices. Then, the recent fundamental advance of microfluidic vias and their applications, e.g. nested bioarrays and autoregulators, are described in greater detail. High-throughput microfluidic immunoassays are discussed as a basis for point-of-care biomedical diagnostics. The next generation of devices is speculated to involve the integration of orthogonal functionalities within the same chip. Such integration will enable overall system miniaturization, fast efficient data acquisition, increased throughput, decreased costs, and new analytical capabilities. Finally, the associated physical, biochemical, and technological challenges are discussed.

Motility of eukaryotic cells is essential for many biological processes such as embryonic development or tissue renewal, as well as for the function of the immune and nervous systems. If misregulated, motility plays an important part in diverse diseases such as cancer, osteoporosis, and mental retardation.

Cell migration over surfaces is an integrated chemical and physical process involving the cytoskeleton and its mechanical interaction with the substrate through discrete adhesion regions. Precise quantitative knowledge of the bio-physical processes involved in cell migration is limited. Better measurements are needed to ultimately build models with predictive capabilities. The free-living soil amoeba Dictyostelium has proven to be a valuable model system for the investigation of cell motility with extensive similarities to higher eukaryotes in general, and leukocytes in particular.

We present an improved force cytometry method and apply it to the analysis of the dynamics of the chemotactic migration of the amoeboid form of Dictyostelium discoideum. Our explicit calculation of the adhesion force field takes into account the finite thickness of the elastic substrate and improves the accuracy and resolution compared to previous methods. This enables us to quantitatively study the differences in the mechanics of the migration of wild-type and mutant cell lines up a chemoattractant gradient. The time evolution of the elastic energy exerted by the crawling cells on their substrate is quasi-periodic and can be used as a simple indicator of the different phases of the cell crawling cycle. We find that the period of the elastic energy cycle correlates strongly with the mean velocity of migration regardless of cell type. Furthermore, we show that when cells adhere to the substrate, they exert opposing pole forces that are orders of magnitude higher than the force required to overcome the resistance from their environment.

Hemodynamics factors play key roles in the genesis, progression, diagnosis and treatment of cardiovascular diseases. Computational fluid dynamics (CFD) as a tool has the great potential to improve our understanding of the complicated hemodynamics associated with cardiovascular diseases, and ultimately the treatment of such diseases. My long term research goal is to advance cardiovascular disease research via providing physics insights into physiological and pathological hemodynamics, through developing advanced numerical simulation tools and conducting high-resolution numerical simulations. In this talk I will present the development of an advanced CFD solver aiming at simulating the complicated cardiovascular fluid mechanics under physiological conditions. Numerical methods developed for the complicated flow characteristics, such as complicated geometry, fluid structure interaction, and unsteady pulsatile incoming flow, each of which is very challenging for numerical simulations, will be covered. Numerical investigations of blood flows through prosthetic heart valves as well as an anatomical Total Cavo-Pulmonary Connection (TCPC) Fontan model will be presented and lessons learned from these investigations will be discussed. Concluding remarks will point to my future research directions.

I will discuss a few recent studies on how organisms propel themselves through water, focusing on the appendages that allow them to do so efficiently. I will begin with fish fins, which have evolved over millions of years in a convergent fashion, leading to a highly-intricate fin-ray structure that is found in half of all fish species. This fin ray structure gives the fin flexibility plus one degree of freedom for shape control. I will present a linear elasticity model of the fin ray, based on experiments performed in the Lauder Lab in Harvard's Biology department.

In conjunction with this work, I will present numerical simulations of a fully-coupled fin-fluid model, based on a new method for computing the dynamics of a flexible bodies and vortex sheets in 2D flows. The simulations are applied to the most common mode of fish swimming, based on tail fin oscillations. In the passive case, an optimal flexibility for thrust is identified, and we consider also the optimal distribution of flexibility, with reference to recent measurements of tapering of insect wings and fish fins. We also briefly present work on fundamental instabilities of a flexible body aligned with a flow (the "flapping flag" problem).

I will then discuss work on the role of bumps on the leading edge of humpback whale flippers, in collaboration with Ernst van Nierop and Michael Brenner at Harvard. Bumps have been shown in wind tunnels to increase the angle of attack at which flippers lose lift dramatically, or "stall." This stall-delay is thought to enable greater agility. In this study we propose an aerodynamic mechanism which explains why the lift curve flattens out as the amplitude of the bumps is increased, leading to potentially desirable control properties.

Finally, I will briefly describe results on a recent problem in self-assembly: the formation of 3D structures from flat elastic sheets with embedded magnets. The ultimate utility of this method for assembly depends on whether it leads to incorrect, metastable structures. We examine how the number of metastable states depends on the sheet shape and thickness. Using simulations and the theory of dislocations in elastic media we identify out-of-plane buckling as the key event leading to metastability. The number of metastable states increases rapidly with increasing variability in the boundary curvature and decreasing sheet thickness.

Dept of Mechanical Engineering and Applied Mechanics, University of Pennsylvania

“Polymeric Materials: Overall Behavior, Microstructure Evolution, and Stability”

Polymeric materials are currently used in numerous commercial and military applications, and have shown great promise for utilization in various new technologies, especially in the medical and aerospace industry. There is then a practical, as well as theoretical, need to understand the connection between the underlying microstructure of polymeric materials and their mechanical and physical properties, and how the latter may be enhanced with changes in the former.

Here, I will present an analytical, nonlinear homogenization framework for determining the overall response of polymeric composites subjected to finite deformations. This theory is not only able to capture the macroscopic response of these composites, but is powerful enough as to yield estimates for the onset of their macroscopic failure. The framework accounts for the evolution of the underlying microstructure, which results from the finite changes in geometry induced by the applied loading. This point is key as the evolution of the microstructure can have a significant geometric softening (or stiffening) effect on the overall response of the material, which, in turn, may lead to the possible development of macroscopic instabilities.

The main concept behind these nonlinear homogenization methods is the construction of suitable variational principles utilizing the idea of a “linear comparison composite,” which allows for the conversion of available linear homogenization estimates into analytical estimates for the large-deformation overall response of the nonlinear polymeric composites. Following the presentation of the general theory, I will show applications for reinforced and porous rubbers, as well as for thermoplastic elastomers. The subtle interplay between the evolution of the relevant microstructural variables (i.e., porosity, particle rotation) and the overall behavior and macroscopic failure in these materials will be put into evidence for all three specific cases, although the various mechanisms identified should be relevant in other polymer-based systems, including smart materials.

“Engineering New Treatments for Cardiovascular Disease via Optimal Design and Physiologic Simulation”

Rigorous modeling and optimization of treatments for cardiovascular disease according to engineering principles provide a framework for testing new surgeries and interventions at no risk to patients. Ultimately these tools have the potential to complement doctors' clinical judgement and experience to improve outcomes for patients suffering from both congenital and acquired heart disease. In this talk I will discuss the application of computational fluid dynamics to the Fontan surgery, a treatment for severe congenital heart defects in which a patient is born with only one functioning ventricle. Patient specific geometric models were used to evaluate the performance of current Fontan surgical designs by quantifying fluid-mechanical efficiency under physiologic conditions including rest, graded exercise, and respiration (Marsden, et. al, Ann Biomed Eng, 35(2), 2007). This work inspired a new "y-graft" design of the Fontan surgery. Evaluation of the new design demonstrates improved efficiency and lower Fontan pressures.

Optimization is commonly used in engineering industry for design, but neither simulation or optimization are currently used to test surgical designs in advance of trying them on patients. Optimization of new surgical designs for patient specific models such as the Fontan surgery requires methods that are appropriate for expensive fluid mechanics problems with little or no gradient information. Efficient derivative-free surrogate-based optimization methods have recently been successful in reducing aerodynamic noise generated by airfoils in turbulent flow (Marsden, et. al, J Fluid Mech, 572, 2007). A similar set of tools is now being applied to fully couple optimization algorithms with time-dependent simulations of blood flow. I will present three model problems for optimization that are representative of important cardiovascular problems, a stenosis, a vessel bifurcation and an end-to-side anastomosis. Next, I will discuss the application of optimization tools in future work for the design of the Fontan surgery. Finally, I will describe the potential broad impact of optimization in designing devices and surgical procedures for congenital heart disease, coronary artery disease, and peripheral vascular disease.

Amorphous metals are regarded as a new class of materials, as they differ fundamentally from conventional metals in their atomic structure, mechanical properties, and fundamental solidification behavior. Metallic glass-forming alloys vitrify (become configurationally “frozen”) upon cooling in the undercooled liquid state to form bulk glasses. Compared to conventional crystalline metals, amorphous metals exhibit very high strength, specific strength, and elastic strain limit, along with unusual combinations of other engineering properties. Yet their moderate toughness combined with a lack of ductility has, to a large extent, limited the exploitation of amorphous metallic materials in traditional structural engineering applications. Their ability to relax and flow when energetically activated, however, gives rise to an inherent “thermoplastic” micro-fabricability, which provides opportunities for the exploitation of amorphous metals in other attractive non-conventional engineering applications such as micro-electromechanical device (MEMS) or cellular metallic structure (metal foam) applications. A recently developed statistical-mechanics model describing the inhomogeneous random structure of the metallic glass which determines and controls the mechanics of failure and the thermodynamics of relaxation and flow will be introduced, and recent experimental and computational breakthroughs will be presented. Moreover, recent technological advances in the areas of MEMS and metal foams will be outlined, with particular emphasis given to cellular structure applications such as lightweight armor material for blast protection, scaffold material for property-matched biomedical implant, and space structure material for micrometeorite shielding.

Cooperative robotic networks present new challenges that lie at the confluence of communication, computing, sensing, and control. A lot is known about the individual components of these networked systems, and yet novel theoretical developments are needed to integrate these components into autonomous networks with predictable behavior. The objective of this talk is to present recently developed modeling, analysis, and design tools for motion coordination of cooperative networks. In our exposition, we pay special attention to the characterization of the correctness, performance, and cost of coordination algorithms. We illustrate our technical approach in disk-covering, sphere-packing, and visibility-based deployment problems as well as in aggregation and consensus scenarios.

In the field of cardiology, our current ability to accurately detect diastolic dysfunction is unsatisfactory due to the lack of an effective diagnostic index. Currently, assessments of diastolic dysfunction are based on echocardiographic measurements that are assumed to be correlated with progression from mild dysfunction to more severe disease. However, relying on existing ultrasonic indices for diagnosis of diastolic dysfunction leads us to underestimate the progress of dysfunction. This type of confusion especially arises during the conversion from mild to moderate stages of disease and hides the progress of the dysfunction (pseudonormalization). Therefore, the conventional indices act as false indicators when dysfunction is progressing from reversible to irreversible stages. This was a motivation to work on developing new approaches for evaluation of cardiac function. In this seminar, I will talk about how experimental mechanics and modeling techniques can help us better approach the problem of cardiac dysfunction.

The presence of vortical flow structures that develop along with a strong propulsive jet during diastole in a normal left ventricle has been demonstrated by different imaging modalities. Thus, physical characteristics of these vortices may provide more effective indices of diastolic function than existing ones. Process of formation of a vortex ring in fluid mechanics literature is described by a dimensionless number called “formation time”. Based on the fact that the normal characteristics of the trans-mitral flow change in the course of different ventricular disorders and these changes are reflected on the vortex formation process in certain ways, I show that formation time can be used as a global index that quantifies diastolic function.

In the final part of this seminar, I will present a new generation of percutaneous heart valves that we designed, and will discuss the recent progress achieved in prototyping this type of heart valve, and its method of delivery.

“Stress-Induced Martensitic Phase Transformation and Fracture in Thin Sheets of Nitinol”

Nickel-Titanium, commonly referred to as nitinol, is a shape-memory alloy with numerous applications due to its superelastic nature and its ability to revert to a previously defined shape when deformed and then heated past a set transformation temperature. While the crystallography and the overall phenomenology are reasonably well understood, much remains unknown about the deformation and failure mechanisms of these materials. These latter issues are becoming critically important as nitinol is being increasingly used in medical devices and space applications.

The talk will describe the investigation of the deformation and failure of nitinol using an in-situ optical technique called Digital Image Correlation (DIC). With this technique, full-field quantitative maps of strain localization are obtained for the first time in thin sheets of nitinol under tension. These experiments provide new information connecting previous observations on the micro- and macro- scale. They show that martensitic transformation initiates before the formation of localized bands, and that the strain inside the bands does not saturate when the bands nucleate. The effect of rolling texture, the validity of the widely used resolved stress transformation criterion, and the role of geometric defects are examined. A detailed investigation of fracture will be presented, including the observed saturation and transformation zones around the cracktip, as well as a determination of the K_C value for thin sheets of nitinol. A discussion of these results in the context of theoretical models will be provided.

I will discuss two classes of multifunctional materials. First, I present my work on polymer composites with tailored electromagnetic (EM) functionalities. Inspired by biological systems, I seek to develop engineering materials that exhibit multiple functionalities in addition to their structural integrity, emphasizing the results of my own work on EM properties. I examine several techniques for numerical and analytical modeling of periodic media to design and predict their overall behavior. These designs were then fabricated and their responses were experimentally measured. I will discuss how I have extracted the overall EM parameters. Examples include fiber-reinforced polymer composites with embedded arrays of straight wires or coils, for which the overall ε of the medium was matched with that of the free space or even rendered negative within microwave frequencies. The coil medium can exhibit chiral response. Solutions for eliminating this behavior as well as a method for calculation of the bianisotropic material parameters are presented. By reducing the length scale, I show that a polymer film with embedded nano-strips of gold can demonstrate negative ε in the infrared regime. An example of a structural composite is presented for which μ is altered and is turned negative within the GHz band.

In the second part of my talk, I present a nonlinear pressure- and temperature-dependent viscoelastic model for polyurea, an elastomeric block copolymer. It has been experimentally observed that a steel–elastomer bilayer may show improved resistance to failure under impulsive loads. I show the extensive set of experiments I have conducted on this material, including the relaxation moduli which are used in a time-temperature equivalence model to predict the high-strain rate response. The model is verified through its application to the Hopkinson-bar tests. I have developed a computational algorithm for this model, integrated it into an explicit finite element solver, and used it to reproduce the results of pressure-shear plate impact tests performed at Brown University. This model is currently being extensively used for prediction of the response of metal–polymer bilayer impact tests, here at UCSD as well as at several other research institutions.

The current technology of high-power lasers generates the high energy density (HED) environment in a laboratory. Energy densities in excess of 10¹² erg/cc exist in the core of stars and, until recently, could be reproduced only through nuclear explosions. Energy densities of 10¹² erg/cc correspond to a pressure of 1 megabar (Mbar) = 10⁶ atmospheres. For example, a milligram of hydrogen at temperature of 10,000,000 Cº confined within 1 cc is at about 1 Mbar of pressure. At such high temperatures, matter is in the form of a plasma, where atoms split into electrons and ions.

My research interest is the physics in high energy density (HED) matters created by ultra-short ultra-intense laser irradiation. The laser energy is compressed in sub-picosecond (< 10^-12 sec) and its power exceeds 100 terrawatt = 10¹⁴ watt instantaneously, which is greater than the energy consumption power on the globe. Such enormous laser power heats a matter up to 10¹² erg/cc immediately in a picosecond, and particle motion in the matter becomes relativistic. This extreme matter is similar to the core of stars. Therefore the HED physics in hot dense matter created by the ultra-short ultra-intense laser pulse is important and also interesting for understanding the physics inside the Sun. The same physics is also applicable to control the HED matter to realize fusion energy, ultra-fast super blight x-ray sources or compact particle accelerator in future.

Because the high power laser created HED environment happens in a very short time, ~ picoseconds. the information which we can get from diagnostics in the experiment are limited, e.g. x-ray emission, neutron yield, etc. A large-scale computer simulation is necessary to interpret the experiments and infer the HED environment. One of my research goals is making a theoretical/numerical model of the laser-matter interaction as a virtual laboratory on computer memories. In this talk, I would like to introduce the simulation model and then present applications of HED physics by ultra-intense laser light including the experimental data.

Sandwich panels with topologically optimized core architectures possess a number of interesting properties, e.g. high specific stiffness and strength, superior resistance to impact loading, potential for active cooling and ability to morph shape against large restraining forces with low resistance to actuation. More interestingly, some of these benefits can be attained simultaneously, resulting in multifunctional structures. In this talk, I will explore the possibility of using actively cooled, all-metallic sandwich panels as combustion chamber liners for hypersonic vehicles. An analytical model, verified by a number of finite elements calculations, is developed with a two-fold scope: (i) optimize the panel geometry for minimum weight subject to all the necessary design constraints, and (ii) rapidly explore the feasibility of various materials. When applied to Mach 7 hydrocarbon-powered hypersonic vehicles, the model clearly shows that several optimally designed metallic solutions are competitive with high-temperature ceramic matrix composites; the conclusion can change at higher Mach number. In closing, I will introduce the possibility to apply some of the benefits of optimally designed sandwich structures to micro- and meso-scale structures, in particular in the context of robust, high-authority microactuators, morphing microstructures and propulsion devices for Micro Aerial Vehicles (MAV).