Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations

This article describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, and noncontact technique for the measurement of curvatures and nonuniform curvature changes in film-substrate systems. The technique is applied to the study of curvature fields in thin Al films (6 mum) deposited on thin circular silicon wafers (105 mum) of "large" in-plane dimensions (50.8 mm in diameter) subjected to thermal loading histories. The loading and geometry is such that the system experiences deformations that are clearly within the nonlinear range. The discussion is focused on investigating the limits of the range of the linear relationship between the thermally induced mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and finally, on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch strain. Results obtained on the basis of both simple models and more-detailed finite-element simulations are compared with the full-field CGS measurements with the purpose of validating the analytical and numerical models

Influence of Interface Scattering on Shock Waves in Heterogeneous Solids

In heterogeneous media, the scattering due to interfaces between dissimilar materials play an important role in shock wave dissipation and dispersion. In this work the influence of interface scattering effect on shock waves was studied by impacting flyer plates onto periodically layered polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites. The experimental results (using VISAR and stress gauges) indicate that the rise time of the shock front decreases with increasing shock strength, and increases with increasing mechanical impedance mismatch between layers; the strain rate at the shock front increases by about the square of the shock stress. Experimental and numerical results also show that due to interface scattering effect the shock wave velocity in periodically layered composites decreases. In some cases the shock velocity of a layered heterogeneous composite can be lower than that of either of its components

Excited state entanglement in homogeneous fermionic chains

We study the Renyi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free, translational invariant Hamiltonian. In order to analytically compute the entropy we use two technical tools. The first one is used to reduce logarithmically the complexity of the problem and the second one to compute the R\'enyi entropy of the chosen subsystem. We introduce new strategies to perform the computations, derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome. Finally we discuss the physical interpretation of our results and generalise them to compute the entanglement entropy for a fragment of a fermionic ladder.Comment: 31 pages, 1 table, 8 figures. Final version published in J. Phys. A. References and section added. Typos correcte

2018 Timoshenko Medal Acceptance Lecture: Academic Family

Dedicated to my immediate academic family, my wonderful graduate students and postdocs and Stefan Timoshenko's academic great, great, great, great, great, great grandchildren. Dear friends, I was brought up in Greece to believe in the power of families. As a result families are very important to me and so are all of you, whom I consider to be my extended academic family. This is exactly the reason for which I feel so excited and honored to receive the Timoshenko Medal in front of you tonight since I truly consider all of you, working in the general area of mechanics at all length and time scales, as my cherished academic brothers and sisters, parents and grandparents. So please allow me to make “Academic Family” my theme for tonight, because I truly feel that in addition to inspiration and creativity, collegiality and mentoring are the two most important corner stones of our profession

Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

Million frames per second infrared imaging system

An infrared imaging system has been developed for measuring the temperature increase during the dynamic deformation of materials. The system consists of an 8×8 HgCdTe focal plane array, each with its own preamplifier. Outputs from the 64 detector/preamplifiers are digitized using a row-parallel scheme. In this approach, all 64 signals are simultaneously acquired and held using a bank of track and hold amplifiers. An array of eight 8:1 multiplexers then routes the signals to eight 10 MHz digitizers, acquiring data from each row of detectors in parallel. The maximum rate is one million frames per second. A fully reflective lens system was developed, consisting of two Schwarszchild objectives operating at infinite conjugation ratio. The ratio of the focal lengths of the objectives determines the lens magnification. The system has been used to image the distribution of temperature rise near the tip of a notch in a high strength steel sample (C-300) subjected to impact loading by a drop weight testing machine. The results show temperature rises at the crack tip up to around 70 K. Localization of temperature, and hence, of deformation into "U" shaped zones emanating from the notch tip is clearly seen, as is the onset of crack propagation

Super-roughening as a disorder-dominated flat phase

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219 (2000)], we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter

Interpretation of optical caustic patterns obtained during unsteady crack growth: an analysis based on a higher-order transient expansion

The optical caustic method is re-examined considering the presence of transient effects. Based on the higher-order asymptotic expansion provided by Freund and Rosakis, regarding the stress field near a non-uniformly propagating crack tip, the caustic mapping and the initial curve equations are derived. The dynamic stress intensity factor, K^d_I(t), is related to experimentally measurable quantities of the caustic pattern by an explicit expression. It is shown that the classical analysis of caustics is a special case of the new interpretation method. The Broberg problem is used as an example problem to check the feasibility of analysing caustics in the presence of higher-order transient terms. It is shown that the caustic patterns are sensitive to transient effects, and that use of the classical analysis of caustics in the interpretation of the optical patterns for this problem may result in large errors in the value of the stress intensity factor, especially at short times after initiation