A Mechanical Model for Elastic Fiber Microbuckling

A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (<0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed

Damage progression in compressively loaded laminates containing a circular cutout

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76038/1/AIAA-10597-113.pd

An atlas of monthly mean distributions of SSMI surface wind speed, AVHRR/2 sea surface temperature, AMI surface wind velocity, TOPEX/POSEIDON sea surface height, and ECMWF surface wind velocity during 1993

The following monthly mean global distributions for 1993 are presented with a common color scale and geographical map: 10-m height wind speed estimated from the Special Sensor Microwave Imager (SSMI) on a United States (U.S.) Air Force Defense Meteorological Satellite Program (DMSP) spacecraft; sea surface temperature estimated from the Advanced Very High Resolution Radiometer (AVHRR/2) on a U.S. National Oceanic and Atmospheric Administration (NOAA) satellite; 10-m height wind speed and direction estimated from the Active Microwave Instrument (AMI) on the European Space Agency (ESA) European Remote Sensing (ERS-1) satellite; sea surface height estimated from the joint U.S.-France Topography Experiment (TOPEX)/POSEIDON spacecraft; and 10-m height wind speed and direction produced by the European Center for Medium-Range Weather Forecasting (ECMWF). Charts of annual mean, monthly mean, and sampling distributions are displayed

Elastic forces that do no work and the dynamics of fast cracks

Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is used to propose a universal scenario, in which three dimensionality is essential, for the dynamic instability of fast cracks in thin brittle materials.Comment: 8 pages Latex, 1 Postscript figur

Assessment of digital image correlation measurement errors: methodology and results

Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the field of experimental mechanics, but they still suffer from a lack of information about their metrological performances. To assess the performance of DIC techniques and give some practical rules for users, a collaborative work has been carried out by the Workgroup “Metrology” of the French CNRS research network 2519 “MCIMS (Mesures de Champs et Identification en Mécanique des Solides / Full-field measurement and identification in solid mechanics, http://www.ifma.fr/lami/gdr2519)”. A methodology is proposed to assess the metrological performances of the image processing algorithms that constitute their main component, the knowledge of which being required for a global assessment of the whole measurement system. The study is based on displacement error assessment from synthetic speckle images. Series of synthetic reference and deformed images with random patterns have been generated, assuming a sinusoidal displacement field with various frequencies and amplitudes. Displacements are evaluated by several DIC packages based on various formulations and used in the French community. Evaluated displacements are compared with the exact imposed values and errors are statistically analyzed. Results show general trends rather independent of the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the uncertainty with the parameters of the algorithms, such as subset size, gray level interpolation or shape functions, is discussed

Fundamental Studies Relating to Systems Analysis of Solid Propellants : Progress Report No. 5 - GALCIT 101, Subcontract No. RU- 293, October l, 1959-December 31, 1959

Previous reports of this series have attempted to define some of the important parameters affecting the structural integrity of solid propellant rocket grains. Three general areas have been discussed, namely material properties, analytical procedures, and criteria for mechanical failure. This particular report is devoted to a more detailed examination of the properties of a filled viscoelastic resin, and their representation by appropriate mechanical models. In addition, a comparison of two methods of computing viscoelastic strains in a pressurized cylinder is presented. In the category of material properties, linear viscoelastic model theory is reviewed, and certain important relations among sets of experimental data are deduced. A justification for the application of this theory is provided by the analytic representation of available dynamic data in terms of a well-known distribution function. Since the inception of this work additional experimental data on propellants has become available. In the category of analytical procedures, the usual approach of representing material properties by a four-element model, as determined from the dynamic data in a limited frequency range, is compared with the more sophisticated Fourier transform method in which the entire frequency range is utilized. The two approaches are applied to calculate the viscoelastic hoop strain at the inner boundary of an internally pressurized infinitely long hollow cylinder subjected to a ramp-type pressure pulse. In this example, the dilatation is assumed elastic or frequency independent and the distortion viscoelastic. In the following quarter, primary effort will be devoted to the determination of a criterion for mechanical failure of propellants. Two steps are involved. One is the analytical representation of ultimate strain as a function of temperature on strain rate by means of a mechanical model. In addition to the usual distribution of relaxation (or retardation) times, this model will be supplied with a distribution of ultimate strain. Step two involves the choice of a suitable criterion for compounding ultimate strain or ultimate stress components into a single parameter, which, when exceeded at a given rate and temperature, denotes the onset of fracture or mechanical failure

The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories

We construct a generalized cusped Wilson loop operator in N = 6 super Chern-Simons-matter theories which is locally invariant under half of the supercharges. It depends on two parameters and interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines, representing a natural generalization of the quark-antiquark potential in ABJ(M) theories. For particular choices of the parameters we obtain 1/6 BPS configurations that, mapped on S^2 by a conformal transformation, realize a three-dimensional analogue of the wedge DGRT Wilson loop of N = 4. The cusp couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bifundamental representation of the U(N)xU(M) gauge group and its expectation value is expressed as the holonomy of a suitable superconnection. We discuss the definition of these observables in terms of traces and the role of the boundary conditions of fermions along the loop. We perform a complete two-loop analysis, obtaining an explicit result for the generalized cusp at the second non-trivial order, from which we read off the interaction potential between heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility to explore in the three-dimensional case the connection between localization properties and integrability, recently advocated in D = 4.Comment: 53 pages, 10 figures, added references, this is the version appeared on JHE

Small deformations of supersymmetric Wilson loops and open spin-chains

We study insertions of composite operators into Wilson loops in N=4 supersymmetric Yang-Mills theory in four dimensions. The loops follow a circular or straight path and the composite insertions transform in the adjoint representation of the gauge group. This provides a gauge invariant way to define the correlator of non-singlet operators. Since the basic loop preserves an SL(2,R) subgroup of the conformal group, we can assign a conformal dimension to those insertions and calculate the corrections to the classical dimension in perturbation theory. The calculation turns out to be very similar to that of single-trace local operators and may also be expressed in terms of a spin-chain. In this case the spin-chain is open and at one-loop order has Neumann boundary conditions on the type of scalar insertions that we consider. This system is integrable and we write the Bethe ansatz describing it. We compare the spectrum in the limit of large angular momentum both in the dilute gas approximation and the thermodynamic limit to the relevant string solution in the BMN limit and in the full AdS_5 x S^5 metric and find agreement.Comment: 40 pages, amstex, 4 figures. V2: Corrected eqn (2.14) and some equations in section 5. Version to appear in JHE