Vertex Effect in Strain-Softening Concrete at Rotating Principal Axes

The inelastic behavior of concrete for highly nonproportional loading paths with rotating principal stress axes is studied. Test cylinders are first loaded in compression under uniaxial stress and then torsion is applied at constant axial displacement. Proportional compressive-torsional loading tests are also carried out for comparison. The tests demonstrate that the response of concrete for load increments parallel in the stress space to the current yield surface is highly inelastic (i.e., much softer than elastic) in the peak load range and especially in the postpeak range. The classical tensorial models of plasticity type incorrectly predict for such load increments the elastic stiffness. The experiments are simulated by three-dimensional finite element analysis using the microplane model M4, in which the stress-strain relations are characterized not by tensors but by vectors of stress and strain on planes of various orientations in the material. It is shown that the observed vertex effect is correctly predicted by this model, with no adjustment of its material parameters previously calibrated by other test results. The experiments are also simulated by a state-of-the-art fracture-plastic model of tensorial type and it is found that the vertex effect cannot be reproduced at all, although an adjustment of one material parameter suffices to obtain a realistic postpeak slope and achieve a realistic overall response. What makes the microplane model capable of capturing the vertex effect is the existence of more than 60 simultaneous yield surfaces. Capturing the vertex effect is important for highly nonproportional loading with rotating principal stress axes, which is typical of impact and penetration of missiles, shock, blasts, and earthquake.     

Size Effect on Strength of Quasibrittle Structures with Reentrant Corners Symmetrically Loaded in Tension

The effect of V-notches (or reentrant corners) on fracture propagation has been analyzed for brittle materials, but not for quasibrittle materials such as concrete, marked by a large material characteristic length producing a strong size effect transitional between plasticity and linear elastic fracture mechanics. A simple size effect law for the nominal strength of quasibrittle structures with symmetrically loaded notches, incorporating the effect of notch angle, is derived by asymptotic matching of the following five limit cases: (1) Ba?ant’s size effect law for quasibrittle structures with large cracks for notch angle approaching zero; (2) absence of size effect for vanishing structure size; (3) absence of size effect for notch angle approaching π; (4) plasticity-based notch angle effect for vanishing size; and (5) the notch angle effect on crack initiation in brittle structures, which represents the large-size limit of quasibrittle structures. Accuracy for the brittle large-size limit, with notch angle effect only, is first verified by extensive finite-element analyses of bodies with various notch angles. Then a cohesive crack characterized by a softening stress-separation law is considered to emanate from the notch tip, and the same finite-element model is used to verify and calibrate the proposed law for size and angle effects in the transitional size range in which the body is not far larger than Irwin’s material characteristic length. Experimental verification of the notch angle effect is obtained by comparisons with Dunn et al.’s extensive tests of three-point-bend notched beams made of plexiglass (polymethyl methacrylate), and Seweryn’s tests of double-edge-notched tension specimens, one set made of plexiglass and another of aluminum alloy.     

Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress

The first part of this two-part study presents a new improved microplane constitutive model for concrete, representing the fourth version in the line of microplane models developed at Northwestern University. The constitutive law is characterized as a relation between the normal, volumetric, deviatoric, and shear stresses and strains on planes of various orientations, called the microplanes. The strain components on the microplanes are the projections of the continuum strain tensor, and the continuum stresses are obtained from the microplane stress components according to the principle of virtual work. The improvements include (1) a work-conjugate volumetric deviatoric split—the main improvement, facilitating physical interpretation of stress components; (2) additional horizontal boundaries (yield limits) for the normal and deviatoric microplane stress components, making it possible to control the curvature at the peaks of stress-strain curves; (3) an improved nonlinear frictional yield surface with plasticity asymptote; (4) a simpler and more effective fitting procedure with sequential identification of material parameters; (5) a method to control the steepness and tail length of postpeak softening; and (6) damage modeling with a reduction of unloading stiffness and crack-closing boundary. The second part of this study, by Caner and Ba?ant, will present an algorithm for implementing the model in structural analysis programs and provide experimental verification and calibration by test data.     

Application of the reaction kinetics and dispersion model to gas-solid reactors for removal of sulfur dioxide from flue gas

The conversions of a reactive, micro-grained limestone were studied in terms of exposure time and concentration of sulfur dioxide in the flue gas. The rates of the sulfation reaction were correlated as a function of the conversion of calcium oxide to sulfate and concentration of sulfur dioxide in the gas phase. In comparison with active sodium carbonate the sulfation of limestone particles proceeds at the rate which is substantially lower than the sulfation rate of soda particles.The empirical kinetic equation developed in this study is further applied in a two-phase dispersion model of simplified non-ideal flow behavior of the gas and solid in the reactor. The model can serve a rational basis for the conceptual design of a suitable contacting apparatus. Numerical solutions of the model equations outline possibilities and limitations of the dry lime process for the removal of sulfur dioxide from hot flue gas.     

Sampling analysis of concrete structures for creep and shrinkage with correlated random material parameters

The latin hypercube sampling method, which represents the most efficient way to determine the statistics of the creep and shrinkage response of structures, has previously been developed and used under the assumption that the random parameters of the creep and shrinkage prediction model are mutually independent. In reality they are correlated. On the basis of existing data, this paper establishes, by means of the method of maximum likelihood, the joint multivariate probability distribution of the random parameters involved, tests the hypothesis of mutual dependence of parameters on the basis of the χ²-distribution, and generalizes the latin hypercube sampling method to the case of correlated multinormal random parameters. The generalization is accomplished by an orthogonal matrix transformation of the random parameters based on the eigenvectors of the inverse of the covariance matrix. This yields a set of new random parameters which are uncorrelated (independent) and can be subjected to the ordinary latin hypercube sampling, with samples of equal probabilities. Numerical examples of statistical prediction of creep and shrinkage effects in structures confirm the practical feasibility of the method and reveal a good agreement with the scatter observed in some previous experiments.     

Size Effect on Strength of Floating Sea Ice under Vertical Line Load

The size effect on the nominal strength of a floating ice plate subjected to a vertical uniform line load is analyzed. The cracks produced by the load, which are parallel to the load line, are treated as softening inelastic hinges. The problem is one dimensional in the direction normal to the load line, equivalent to a beam on elastic foundation provided by buoyancy of ice in water. The softening moment-rotation diagram of inelastic hinges is simplified as linear and its dependence on structure size (ice thickness) is based on the energy dissipated by fracture. For thick enough plates, no two hinges (on one side of the line load) can soften simultaneously, in which case a simple analytical solution is possible. In that case, the load-deflection diagram has multiple peaks and troughs and consists of a sequence of spikes that get progressively sharper as the plate thickness increases. In terms of a dimensionless nominal strength, the effect of a finite fracture process zone at ice surface leads to an up-and-down size effect plot, such that each load peak decreases with the size at first but then asymptotically approaches a rising asymptote of the type (thickness)1/4 (which implies a reverse size effect, caused by buoyancy). The energy dissipation when the crack in the hinge gets deep causes a strong monotonic size effect, such that the dimensionless troughs between two spikes, in the case of thick enough plate, decrease asymptotically as (thickness)?1/2. For thin enough plates, more than one hinge soften simultaneously and, in the asymptotic case of vanishing ice thickness, the plasticity solution, which has no size effect, is approached. In the intermediate size range with hinges softening simultaneously, the exact solution is complicated and only approximate formulas for the size effect are possible. They are constructed by asymptotic matching.     

Improved prediction model for time-dependent deformations of concrete: Part 7—Short form of BP-KX model,statistics and extrapolation of short-time data

For structures that do not have a high sensitivity to creep or for preliminary design of any structures, practising engineers demand a short formula for predicting the material creep properties. Such a formula is given in the present addendum to a previous six-part paper. It is based on optimal fitting of the previously published log-double power law to the formulae of the BP-KX model. A simple formula giving directly the compliance function rate is also presented. Finally, a simple method of improving the predictions on the basis of short-time measurements is described, and tables giving the statistics of the deviations of the prediction formulas of the simplified model and its short form from the data in the literature are presented.     

Compatibilization efficiency of styrene‐butadiene block copolymers as a function of their block number

Effect of block number in linear styrene‐butadiene (SB) block copolymers (BCs) on their compatibilization efficiency in blending polystyrene (PS) with polybutadiene (PB) was studied. Di‐, tri‐, or pentablocks of SB copolymers as well as their combinations were blended with the mentioned homopolymers; supramolecular structure determined by small angle X‐ray scattering method (SAXS), morphology using scanning electron microscopy (SEM) combined with image analysis (IA), and stress transfer characteristics of the blends were chosen as criteria of compatibilization efficiency of the copolymers used. It was proved that the addition of SB BCs led to remarkably finer phase structure and substantially higher toughness of PS/PB blends. Triblock copolymer showed to be the compatibilizer with higher efficiency than diblock, pentablock, and the di/triblock copolymer mixture. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Live TV subtitling through respeaking with remote cutting-edge technology

Multimedia Tools and Applications - This article presents an original system for live TV subtitling using respeaking and automatic speech recognition. Unlike several commercially available live...