Journal of Engineering Mechanics

High performance, fiber-reinforced composites are identified by their high strength and toughness associated with multiple cracking. If the composite is adequately reinforced, the bridging fibers will transfer the load and multiple cracking will occur when the subsequent transferred load cracks the matrix again. This study investigates the effect of dispersion of fibers on the multiple cracking behavior of fiber-reinforced composites. The electronic speckle pattern interferometry technique is used to record the location of crack initiation, the sequence of the multiple cracking, and the corresponding cracking stresses. Microstructural parameters at each crack location are statistically quantified by the theory of point processes. The size of the fiber-free areas and the fiber clumping are calculated at the crack cross sections. By using linear elastic fracture mechanics, the fracture toughness of the matrix is calculated. A strong relation between the cracking stress and the fiber-free areas in the composite is observed. It is shown that the toughness of the composite depends on the fiber clumping at the first crack cross section.

A high-order analytical model for the analysis of reinforced concrete (RC) beams strengthened with fiber-reinforced plastic (FRP) strips bonded with adhesive layer of variable thickness is presented. The model is based on the closed-form high-order approach, and it provides the means for the analysis of beams retrofitted with generally curved FRP strips and adhesive layers of arbitrary profile. The analysis is comprehensive and includes the local and overall response of the structure. An emphasis is put on the stress concentration that occurs at the edge of the FRP strip and in many cases leads to brittle and sudden failure of the strengthened member. The field equations and the boundary and continuity conditions are derived using the variational principle of virtual work along with the kinematic relations of small deformations. The governing equations of the generally curved FRP strip include large curvatures and are introduced via coordinate transformation from its local curvilinear system into the global Cartesian one. The derived model is used for the investigation of various adhesive profiles and their influence on the shear and vertical normal stresses at the edges of the FRP strip. The results focus on the stress concentrations involved and reveal that proper design and application of the adhesive profile can significantly reduce the edge stresses, thus preventing the brittle mode of failure. The paper is concluded with a summary and recommendations for the analysis, design, and application of the strengthening process.

Linear potential theory is applied to the analysis of wave reflection from a composite porous wave absorber that lies on a solid foundation with a seaward slope. By adopting the mathematical model of wave-induced flow in a porous medium, the interaction between water waves and a porous wave absorber is investigated. An extended linear refraction-diffraction model for surface waves is applied to the sloping region in front of the porous absorber. Using the eigenfunction expansions and the finite-difference method, an analytical study is undertaken to predict the wave reflection from such a composite porous absorber. The reflection behavior is discussed for several wave conditions, and the functional efficiency of this absorber is evaluated. It is noted that the present numerical results agree very well with the experimental results available in the literature.

Buckling of thin cylindrical shell liners used for the stabilization of soft ground tunnels is treated as the buckling of an elastic ring restrained radially and tangentially by an infinite surrounding elastic medium. Stiffness components for the elastic medium are derived and used to provide various levels of approximation for the elastic critical loads and associated modes of the liner when subject to overburden pressure loading. For most practical tunnel liners, elastic buckling is found to occur in modes having relatively short circumferential wavelengths. In these circumstances an approximation introduced into the critical pressure analysis allows both the lowest critical pressure and its associated mode shape to be represented explicitly in terms of a single “soft ground tunnel buckling parameter”; this single composite parameter encapsulates all the relevant ground and liner geometric and material properties. It is this closed-form analytical representation of elastic critical buckling that provides a particularly convenient basis for predicting elastic-plastic failure. When imperfections are introduced, liner collapse and the various forms of ground failure can be modeled by methods analogous to the Ayrton-Perry expression for columns. Two generalized imperfection parameters emerge: one for liner collapse and the other for each of three possible, soft ground, failure modes. It is suggested that the analytical simplicity of the approach should make it an attractive alternative basis for at least the initial, rational, design of soft ground tunnel liners.

Service life of concrete structures is limited by the susceptibility of the reinforcement to corrosion. Oxidation of iron leads to the formulation of various products (such as ferrous and ferric oxides), some of which occupy much greater volume than the original iron that gets consumed by the corrosion process. As corrosion progresses, these products accumulate, thereby generating expansive pressures on the surrounding concrete. The pressure builds up to levels that cause internal cracking around the bar and eventually leads to through cracking of the cover and spalling. Loss of cover marks the end of service life for corrosion-affected concrete structures, because at that stage the reinforcement loses its ability to develop its forces through bond and is no longer protected against further degradation from corrosion. In this paper, a simple analytical model is formulated to demonstrate the mechanical consequences of corrosion-product buildup around the bar. Service life is estimated as the time required for through cracking of the cover, which is identified in the model by a sudden drop of the internal pressure exerted by the corroding bar eventually relaxing to zero. Cracking time is found to be a function of cover, material properties of the surrounding concrete, and rust product, and is controlled by the rate of rust accumulation. In formulating the associated boundary-value problem, the governing equation expressed in terms of radial displacements is discretized using finite differences, whereas cracked concrete is treated as an orthotropic material. Calculated cracking times are correlated against published experimental data. The parametric sensitivity of the model is established with reference to published experimental evidence, and the role of the important design variables in the evolution of this mechanical problem is identified and discussed.

An efficient method is presented for approximate computation of extreme value characteristics of the response of a linear structure subjected to nonstationary Gaussian excitation. The characteristics considered are the mean and standard deviation of the extreme value and fractile levels having specific probabilities of not being exceeded by the random process within a specified time interval. The approximate procedure can significantly facilitate the utilization of nonstationary models in engineering practice, since it avoids computational difficulties associated with direct application of extreme value theory. The method is based on the approximation of the cumulative distribution function (CDF) of the extreme value of a nonstationary process by the CDF of a corresponding “equivalent” stationary process. Approximate procedures are developed for both the Poisson and Vanmarcke approaches to the extreme value problem, and numerical results are obtained for an example problem. These results demonstrate that the simple approximate method agrees quite well with the direct application of extreme value theory, while avoiding the difficulties associated with solution of nonlinear equations containing complicated time integrals.

The complete stress-strain and stress-crack opening response of a concretelike material loaded in tension is examined starting from a series of displacement-controlled tests on notched cylinders, whose end sections were prevented from rotating (fixed platens). The test results refer to two very high-strength cementitious composites (tensile strength f_c ≈ 160–165 MPa) and one “reference” high-strength concrete (f_c ≈ 90 MPa). Their behavior (pseudoelastic up to first cracking and cohesive after crack localization) is analyzed to identify the nonlinear stress-strain and stress-crack opening response and to distinguish it from the structural behavior of the specimens. The ascending branch is modeled by studying the stresses at the notch tip by means of Neuber's approach based on stress concentration factors. As for concrete softening (falling branch), an appropriate cohesive law is introduced. Finally, the structural response associated with progressive cracking is systematically analyzed, and once more, it is shown that the load-displacement relationship obtained in a test is hardly a material property.

Nonlinear relations between the beam displacement and generalized strain measures, which have basic effects on postbuckling behavior of elastic beams, are presented. The complex coupling phenomena associated with the higher order strain terms is reviewed for the special case of planar and rectilinear pinned-pinned beams. Special consideration was made for the physical assumptions used in the various column-beam models. A natural hierarchy results yielding that all the higher order terms can, for a specific beam formulation, be steadily obtained by dissimilar polynomial approximations of the generalized strains. The asymptotic expansions method and the minimum energy criterion are used to perform analytical calculation of the postbifurcation equilibrium path at the neighborhood of a bifurcation point when only a unique buckling mode is assumed to occur. As a result, postbuckling branches are easily obtained even when accounting for both beam centerline extensional deformation and shear strain. They show that the critical load is scarcely affected by the higher order strain terms unlike the postbuckling paths which are found to be very sensitive to them.

This study aims to address the variations of the open-channel flows that are originally kept in a uniform steady state and then slightly perturbed by injecting a periodic lateral inflow. Uses of some transformations and of the Riemann-Green function method would yield a simple discharge solution in an integral form. The results show that hydrographs of both the main flow discharge and the lateral inflow oscillate with the same period but out phase after a time interval. In addition, flows transported in channels with gentler bottom slopes have longer transient times. The shortcoming in using the integral solution suggested in the present investigation is that the Froude numbers of the unperturbed flows must be >1.5.

In this paper, the effects of geometric imperfections on the nonlinear buckling behavior of rigidly jointed single-layer lattice domes under vertical loading have been studied. A commercially available finite-element code has been used. Numerical experiments using varying levels of imperfection, chosen to be of the same forms as various linear buckling eigenmodes, have demonstrated the complexity of the buckling behavior. Lower bounds to the imperfection sensitivity of elastic overall buckling loads have been shown to result from the reduced stiffness analysis which is a simple extension to the classical linear buckling analysis. In addition an alternative elastic and plastic interaction empirical formula based upon the reduced stiffness loads has been seen to predict the lower bounds in the relatively large level of geometric imperfections.

A multizone nonlinear boundary element method is used to simulate the size effect of quasi-brittle materials that are modeled as randomly dispersed particulate composites with randomly distributed microcracks located between the particles and matrix. Usually a series of geometrically similar specimens are used to describe the size effect of materials. In this paper, a one-size specimen method for determining the fracture energy G_f and effective process zone length c_f is proposed and verified by numerical simulation. The specimen used for boundary element simulation is confined to only one shape and one size but with different initial crack lengths. A three-point-bend beam and a compact tension specimen are used to expand the range of brittleness number and therefore increase the degree of confidence of the results. Notchless specimens of the same size are also calculated and used to supplement the data of one-size notched specimens. The shape, size, and location of the fracture process zone caused by development of microcracking are observed. The results of G_f and c_f obtained from the one-size specimen method are compared with a commonly used method and a good agreement is shown.

The uniaxial, hydrostatic, and triaxial tests of saturated cylindrical rock samples are very common in a rock mechanics laboratory. The conventional solution for the mechanical responses of the sample under such testing conditions (an axial load and a confining pressure) is trivial within the elastic range. For saturated samples, however, these elastic solutions can only be applied to the drained or undrained cases, and there has been a lack of transient analyses of cylindrical samples under such tests, taking into account the pore fluid pressure buildup and the coupling effects, especially for samples with low permeability. In this paper, poroelasticity is employed to develop the solution for saturated cylindrical samples subjected to an axial load and a confining pressure. Significant poroelastic effects on the tests were observed through the analyses of a uniaxial test and a triaxial test based on the proposed poroelastic solution. Without consideration of the poroelastic effects, erroneous interpretations of the testing results can be expected.

A new popular method for retrofitting reinforced concrete beams and slabs is to bond fiber-reinforced plastic (FRP) plates to the soffit. An important failure mode for such strengthened members is the debonding of the FRP plate from the member due to high interfacial stresses near the plate ends. Accurate predictions of the interfacial stresses are a prerequisite for designing against debonding failures. In this paper, a theoretical interfacial stress analysis is presented for simply supported beams and slabs bonded with a thin FRP composite or steel plate and subjected to a uniformly distributed load in combination with a uniform bending moment. The analysis leads to an exact closed-form solution, in which a plane stress model is used for beams and a plane strain model is used for slabs. The salient features of the new analysis include the consideration of nonuniform stress distributions in and the satisfaction of the stress boundary conditions at the ends of the adhesive layer. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions in beams and slabs.