Structural assessment of externally flexural strengthened reinforced concrete beam after repaired with polymer mixture

This study investigated the effectiveness of external strengthening technique. The experimental variables were the strengthening material and overlay materials using polymer mixtures. Beams considered in this study are the ones strengthened either with external steel plate or carbon fiber sheet (CFS) bonded to the overlay soffit or with reinforcing rebars in the overlay. An analytical method based on the nonlinear layered finite element method is used to simulate the load–deflection behavior of strengthened beam. The theoretically obtained load–deflection relationships and strains of the strengthened beams are compared to the corresponding experimental values. Efficiencies of the repairing techniques are evaluated by comparing the approximate measures on the cumulative slips. Parametric studies are then obtained using the developed model to investigate the effects of design variables on the overall flexural behavior of the strengthened beam. Simply supported beams under monotonically increasing symmetrical loads are considered exclusively.     

Nanoindentation Experimental Approach and Numerical Simulation of Al/Cr Bilayer Films

The Al/Cr double-layer film structure samples (thickness, 1200 nm) were prepared by the magnetron sputtering method. To investigate the mechanical properties, the samples were measured by using a nanoindentation instrument. The test results showed the nonlinearity and different modes of the main mechanical properties by comparing the macro-scale structure samples with other samples of similar materials. Based on the test, the elastic modulus and hardness of thin film structures can be calculated by considering different loads to conduct multi-point indentations. Meanwhile, the relationships between the mechanical parameters can be investigated based on these Al/Cr double-layer film structure samples. To validate the test, numerical analysis was developed using a finite element method to simulate the loading and unloading process of indentation. The simulation results were compared with the results of experiments to illustrate the validity of both the test and simulation to a certain extent. The investigation builds not only an experimental basis for practical applications for future study, but also supplies a complementary means of verification for theoretical analysis.     

A Numerical Investigation on the Influence of Steel Fiber Shape and Interface Strength in Reinforced Concrete

Not all steel fiber reinforced concrete composites are equally effective in enhancing structural performance. Their mechanical behaviour strongly depends upon the reinforcement morphology as well as the properties of the interface lying between steel reinforcement and concrete matrix. Using bone-shaped short (BSS) steel fibers, instead of conventional straight short (CSS) steel fibers, to reinforce concrete has demonstrated their potential in improving toughness, ductility and energy absorbing capacity under impact significantly and simultaneously. Accomplishing a strong steel–concrete interface leads to a slight increase in composite strength but simultaneously to a significant decrease in its toughness. Due to the sensitivity of steel reinforced concrete performance on these complex geometric and material parameters, the development of a numerical tool capable of simulating accurately the composite mechanical behaviour and thus leading to optimized design solutions is desirable. The physical problem of the present work involves a typical concrete composite uniformly reinforced with steel fibers subjected to tensional loading. A micromechanical non-linear finite element formulation is utilized in order to predict the load transfer characteristics and the failure process. A linear material behaviour is assumed for the steel component; a non-linear multi-crack material response is used to describe concrete while a mix-mode bilinear behaviour is utilized for the interface providing separation of primary material phases. Numerical results are presented in terms of the global design parameters. The influence of the fiber end shape, the interface strength and the fiber volume fraction on the composite strength and toughness is addressed and consequently optimized design preferences arise.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

Commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of Homogeneous type of finite measure

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp (X), 1 ＜ p ＜∞. We give a sufficient condition on the kernel k(x,y) of Tso that when a function b ∈ BMO (X) ,the commutator [b, T] (f) = T (b f) - bT (f) is aounded on spaces Lp for all p, 1 ＜ p ＜∞.     

Finite element prediction of debonding onset in short fiber reinforced polymers incorporating a hybrid interphase region

A robust finite element procedure for investigating damage evolution in short fiber reinforced polymeric composites under external loads is developed. This procedure is based on an axisymmetric unit cell composed of a fiber, surrounding interphase and bulk matrix. The hybrid interphase concept involves a degraded material phase, the extent of which is material and property dependent. One of the most significant features of the model relies on establishment of variable adhesion conditions between the primary material phases. The unit cell is discretized into linearly elastic elements for the fiber and the matrix and interface elements which allow debonding in the fiber–matrix interface. The interface elements fail according to critical stress and critical energy release rate criteria. The tension and shear aspects of failure are uncoupled, although the resulting nonlinear problem is solved implicitly utilizing quasi-static incremental loading conditions. Final failure resulting from saturation and breakage is modeled by the vanishing interface element technique. Details of the propagation of interface cracks and the initiation of debonds are also observed and discussed for various shapes of fiber end. Numerical results reveal an intense effect of the fiber-end geometry on the initial fiber–matrix de-cohesion. The present finite element procedures can generate meaningful results in the analysis of fiber-reinforced composites.     

On group orders of rational points of elliptic curves

We consider elliptic curves without complex multiplication defined over the rationals or with complex multiplication defined over the Hilbert class field of the endomorphism ring. We examine the distribution of almost prime group orders of these curves when reduced modulo a prime ideal.     

Effects of Filler Content on Mechanical Properties of Macroporous Composites

The mechanical properties of hydroxyapatite related macroporous biocomposites (MPBs) are influenced by a number of factors, such as the pore size, the filler content and the properties of the matrix and the inclusion. Failure often occurs when the strength of the implant cannot bear the applied mechanical load. In this study, the effects of filler content on the mechanical properties of MPBs have been investigated. A finite element (FE) unit cell model of a macroporous hydroxyapatite–polyetheretherketone (HA–PEEK) biocomposite structure with uniform and interconnected pores has been constructed. In the FE model, the HA particles were assumed to have random distribution, and particle volume fraction would be varied in the PEEK matrix. The material behaviours of both HA and PEEK have been implemented in the ABAQUS finite element code. HA was modelled to exhibit elastic behaviour and undergo plastic softening to a residual strength when a critical stress was reached, while the PEEK matrix would follow elastic–plastic behaviour. The macroscopic compressive stress–strain relations of the macroporous biocomposite structures have been predicted. Increasing particle volume fraction could lead to an increase in the compressive elastic modulus of the structures but a reduction in the compressive strength. The von Mises stress distribution and the effect of stress concentration in the structures with different filler content are also discussed. The proposed model could provide macro-structural and microscopic information of the macroporous biocomposite structure to the designers in order to facilitate the fabrication of this kind of structure with optimum mechanical properties.     

A numerical modeling for eigenvibration analysis of honeycomb sandwich panels

The eigenvibration properties of honeycomb sandwich panels are investigated in this paper. A new numerical modeling for eigenvibration analysis of the honeycomb sandwich panels is proposed under the assumption that the orthotropic shell and two kinds of beam elements represent face materials, adhesive layers and honeycomb core, respectively. The shell element is also connected to the beam element through the thickness. The effects of geometry of honeycomb core and thickness of face material on the eigenfrequency are examined through the comparisons between finite element simulation and experimental results. It is shown as a result that the eigenvibration properties depend strongly on the face material rigidity and honeycomb core geometry. The implications of the findings for the design of eigenvibration of honeycomb sandwich panels are discussed from the point of view of overall flexural rigidity.     

Effect of Geometry,Loading and Elastic Moduli on Critical Parameters in a Nanoindentation Test in Polymeric Matrix Composites with a Nonhomogeneous Interphase

Fiber nanoindentation models are developed for polymeric matrix composites with nonhomogeneous interphases. Using design of experiments, the effects of geometry, loading and material parameters on the critical parameters of the indentation test such as the load–displacement curve, the maximum interfacial shear and normal stresses are studied. The sensitivity analysis shows that the initial load–displacement curve is dependent only on the indenter type, and not on parameters such as fiber volume fraction, interphase type, thickness of interphase, and boundary conditions. The interfacial tensile radial stresses are not sensitive to indenter type, or to type and thickness of interphase, while the interfacial compressive radial stresses are sensitive mainly to boundary conditions and thickness of interphase; however, the influence of these factors on the interfacial radial stresses can be large. In contrast, the interfacial shear stress is sensitive to all factors, but the influence of the factors is relatively small.