Physics Commons^™

Deformations Of Geometrically Frustrated Elastic Sheets, Meng Xin

Doctoral Dissertations

The wrinkling and buckling of thin solids are common phenomena in our daily life and can be observed in many situations, such as crumpled papers, stretched plastics, compressed metals, clothes on our bodies and even furrowed human skin. Understanding of these phenomena has therefore long drawn interest of scholars. In this thesis, we discuss two buckling problems numerically and analytically. First, we study the wrinkling mechanism of stretched sheets with clamped edges. A central puzzle underlying this canonical example of “tensional wrinkling” has been the origin of compressive stress, which eventually leads to buckling instability. We elucidate the source of …

Numerical Simulation Of Nonlinear Vibrations Of Discrete Mass With Harmonic Force Perturbation, M. Yusupov, B. A. Akhmedov, Olga Karpova

Acta of Turin Polytechnic University in Tashkent

The problem of vibration of a single-mass system under the force excitation of vibration associated with a fixed base by a weightless nonlinear viscoelastic spring is considered. To take into account the rheological properties of the spring material, the Boltzmann-Volterra principle was used. Mathematical models of the problem under consideration are obtained, which are described by integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis, the results obtained are presented in the form of graphs. The influence of nonlinear and rheological properties of a …

The Conundrum Of Relaxation Volumes In First-Principles Calculations Of Charged Defects In Uo₂, Anuj Goyal, Kiran Mathew, Richard G. Hennig, Aleksandr V. Chernatynskiy

Physics Faculty Research & Creative Works

The defect relaxation volumes obtained from density-functional theory (DFT) calculations of charged vacancies and interstitials are much larger than their neutral counterparts, seemingly unphysically large. We focus on UO2 as our primary material of interest, but also consider Si and GaAs to reveal the generality of our results. In this work, we investigate the possible reasons for this and revisit the methods that address the calculation of charged defects in periodic DFT. We probe the dependence of the proposed energy corrections to charged defect formation energies on relaxation volumes and find that corrections such as potential alignment remain ambiguous with …

Geometry, Growth And Pattern Formation In Thin Elastic Structures, Salem Al-Mosleh

Doctoral Dissertations

Thin shells are abundant in nature and industry, from atomic to planetary scales. The mechanical behavior of a thin shell depends crucially on its geometry and embedding in 3 dimensions (3D). In fact, the behavior of extremely thin shells becomes scale independent and only depends on geometry. That is why the crumpling of graphene will have similarities to the crumpling of paper. In this thesis, we start by discussing the static behavior of thin shells, highlighting the role of asymptotic curves (curves with zero normal curvature) in determining the possible deformations and in controlling the folding patterns. In particular, we …

Curvature-Induced Stiffness And The Spatial Variation Of Wavelength In Wrinkled Sheets, Joseph Paulsen, Evan Hohlfeld, Hunter King, Jiangshui Huang, Zhanglong Qiu, Thomas P. Russell, Narayanan Menon, Dominic Vella, Benny Davidovitch

Physics - All Scholarship

Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles—their wavelength—is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments …

Elasticity Of Differentiated And Undifferentiated Human Neuroblastoma Cells Characterized By Atomic Force Microscopy, Shijia Zhao, Alexander B. Stamm, Jeong Soon Lee, Alexei Gruverman, Jung Yul Lim, Linxia Gu

Department of Mechanical and Materials Engineering: Faculty Publications

Human neuroblastoma (SH-SY5Y) cells, with its ability to differentiate into neurons, have been widely used as the in vitro cell culture model for neuroscience research, especially in studying the pathogenesis of Parkinson’s disease (PD) and developing therapeutic strategies. Cellular elasticity could potentially serve as a biomarker to quantitatively distinguish undifferentiated and differentiated SH-SY5Y cells. The goal of this work is to characterize the retinoic acid (RA) induced alternations of elastic properties of SH-SY5Y cells using atomic force microscopy (AFM). The elasticity was measured at multiple points of a single cell. Results have shown that the differentiation of SH-SY5Y cell led …

On The Crumpling Of Thin Sheets, Anne Dominique Cambou

Doctoral Dissertations

The inner walls of mitochondria, cabbage leaves, and even the Himalayas are all examples of thin sheets: objects with a thickness much smaller than their length and width. Despite their differences in size and in material composition, similar patterns emerge when sheets are crumpled or forced into a small three-dimensional space. As the compaction progresses, the deformations focus into increasingly sharper features that look like the network of peaks and creases found on the surface of a balled up piece of paper. In this regime, external forces are straining the membrane, causing the elastic energy to localize while leaving most …

Swelling And Folding As Mechanisms Of 3d Shape Formation In Thin Elastic Sheets, Marcelo A. Dias

Open Access Dissertations

We work with two different mechanisms to generate geometric frustration on thin elastic sheets; isotropic differential growth and folding. We describe how controlled growth and prescribing folding patterns are useful tools for designing three-dimensional objects from information printed in two dimensions. The first mechanism is inspired by the possibility to control shapes by swelling polymer films, where we propose a solution for the problem of shape formation by asking the question, ``what 2D metric should be prescribed to achieve a given 3D shape?'', namely the reverse problem. We choose two different types of initial configurations of sheets, disk-like with one …

Geometries In Soft Matter, Zhenwei Yao

Physics - Dissertations

No abstract provided.

A Locking-Free Hp Dpg Method For Linear Elasticity With Symmetric Stresses, Jamie Bramwell, Leszek Demkowicz, Jay Gopalakrishnan, Weifeng Qiu

Mathematics and Statistics Faculty Publications and Presentations

We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov- Galerkin (DPG) framework. In this framework, both the stress and the displacement ap- proximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.

Exploring Bacterial Nanowires: From Properties To Functions And Implications, Kar Man Leung

Electronic Thesis and Dissertation Repository

The discovery of electrically conductive bacterial nanowires from a broad range of microbes provides completely new insights into microbial physiology. Shewanella oneidensis strain MR-1, a dissimilatory metal-reducing bacterium, produces extracellular bacterial nanowires up to tens of micrometers long, with a lateral dimension of ~10 nm. The Shewanella bacterial nanowires are efficient electrical conductors as revealed by scanning probe techniques such as CP-AFM and STM.

Direct electrical transport measurements along Shewanella nanowires reveal a measured nanowire resistivity on the order of 1 Ω∙cm. With electron transport rates up to 10⁹/s at 100 mV, bacterial nanowires can serve as a …

Elastic And Magnetic Properties Of Tb6fe(Sb,Bi)2 Using Resonant Ultrasound Spectroscopy., David Michael Mccarthy

Masters Theses

Tb6FeSb2 and Tb6FeBi2 are novel rare earth compounds with little prior research. These compounds show high and variable curie temperatures for rare-earth compounds. This has lead to a literature review which includes the discussion of: elasticity, resonance, and magnetism. This review is used to discuss the theory and methodology which can relate these various properties to each other. Furthermore, synthesis, x-ray analysis, and RUS sample preparation of Tb6FeSb2 and Tb6FeBi2 were completed.

Resonant Ultrasound Spectroscopy (RUS) elastic studies were taken for Tb6FeSb2 and Tb6FeBi2 as a function temperature from 5-300K, in various magnetic fields ranging from 0-9T. Tb6FeSb2’s and Tb6FeBi2’s …

Wrinkling, Folding, And Snapping Instabilities In Polymer Films, Douglas Peter Holmes

Open Access Dissertations

This work focuses on understanding deformation mechanisms and responsiveness associated with the wrinkling, folding, and snapping of thin polymer films. We demonstrated the use of elastic instabilities in confined regimes, such as the crumpling and snapping of surface attached sheets. We gained fundamental insight into a thin film's ability to localize strain. By taking advantage of geometric strain localization we were able to develop new strategies for responsive surfaces that will have a broad impact on adhesive, optical, and patterning applications. Using the rapid closure of the Venus flytrap's leafets as dictated by the onset of a snap instability as …

Viscoelastic Flow In Rotating Curved Pipes, Yitung Chen, Huajun Chen, Jinsuo Zhang, Benzhao Zhang

Mechanical Engineering Faculty Research

Fully developed viscoelastic flows in rotating curved pipes with circular cross section are investigated theoretically and numerically employing the Oldroyd-B fluid model. Based on Dean’s approximation, a perturbation solution up to the secondary order is obtained. The governing equations are also solved numerically by the finite volume method. The theoretical and numerical solutions agree with each other very well. The results indicate that the rotation, as well as the curvature and elasticity, plays an important role in affecting the friction factor, the secondary flow pattern and intensity. The co-rotation enhances effects of curvature and elasticity on the secondary flow. For …

Dislocation-Indenter Interaction In Nanoindentation, M. Ravi Shankar, Alexander H. King, Srinivasan Chandrasekar

Alexander H. King

A formulation of dislocation-indenter interaction in two-dimensional, isotropic elasticity is presented. A significant dislocation-indenter interaction is predicted when dislocations are nucleated very close to the indenter. This interaction is expected to have an important influence on dislocation motion and multiplication. Upon nucleation close to the indenter, the dislocations are shown to modify the load, load distribution, and moment acting on the indenter. This effect is seen to vary with the indentation contact length. Further away from the indenter, the indenter-dislocation interaction is shown to be negligible.

Protonium Formation In The P̅-H Collision At Low Energies By A Diabatic Approach, M. Hesse, Anh-Thu Le, C. D. Lin

Physics Faculty Research & Creative Works

We present a diabatization technique in combination with the recently developed hyperspherical close coupling (HSCC) method. In contrast to the strict diabatization, our simple diabatization procedure transforms only sharp avoided crossings in the adiabatic hyperspherical potential curves into real crossings. With this approach, the weak collision channels can be removed from the close-coupling calculations. This method is used to study the antiproton-hydrogen collision at low energies. In the case of a scaled down (anti)proton mass, we show that a 10-channel calculation is enough to obtain converged cross sections at low energies. The results also indicate that protonium formation occurs mostly …

Chemical Bonding, Elasticity, And Valence Force Field Models: A Case Study For Α-Pt2si And Ptsi, Gus L. W. Hart, J. E. Klepeis, O. Beckstein, O. Pankratov

Faculty Publications

We have carried out a detailed study of the chemical bonding for two room-temperature stable platinum silicide phases, tetragonal α-Pt2Si. These elements of the bonding are further analyzed by constructing valence force field models using the results from recent first principles calculations of the six (nine) independent, nonzero elastic constants of α-Pt2Si (PtSi). The resulting volume-, radial-, and angular-dependent force constants provide insight into the relative strength of various bonding elements as well as the trends observed in the elastic constants themselves. The valence force field analysis yields quantitative information about the nature of the chemical bonding that is not …

Tunable Local Polariton Modes In Semiconductors, Michael G. Foygel, Alexey Yamilov, Lev I. Deych, Alexander A. Lisyansky

Physics Faculty Research & Creative Works

We study the local states within the polariton band gap that arise due to deep defect centers with strong electron-phonon coupling. Electron transitions involving deep levels may result in alteration of local elastic constants. In this case, substantial reversible transformations of the impurity polariton density of states occur, which include the appearance/disappearance of the polariton impurity band, and its shift and/or the modification of its shape. These changes can be induced by thermo- and photoexcitation of the localized electron states or by trapping of injected charge carriers. We develop a simple model, which is applied to the O_p center …

Magnetic And Crystallographic Order In Α‐Manganese, A. C. Lawson, Allen C. Larson, M. C. Aronson, S. Johnson, Z. Fisk, Paul C. Canfield, J. D. Thompson, R. B. Von Dreele

Paul C. Canfield

We have made time‐of‐flight neutron diffractionmeasurements on α‐manganese metal. Powder diffraction measurements were made at 14 temperatures between 15 and 305 K, and single crystalmeasurements were made at 15 and 300 K. We found that the crystal structure of α‐Mn is tetragonal below its Néel point of 100 K, with crystal symmetryI4̄2m and magnetic (Shubnikov) symmetry P I 4̄21 c. In agreement with the earlier results of Yamada et al., there are six independent magnetic atoms, and we found that their moments are weakly temperature dependent. The onset of magnetic order causes slight changes in the atomic positions and in …