Journal of Engineering Mechanics

Surface cracks with different orientations have been recognized as a major cause of potential failures of thin metal structures, which are often under biaxial loading. It has been known that, for cracked ductile metals, plasticity results in an easing of stress intensity at the crack front and ultimately increases the total fracture toughness of the metal. To enable the use of linear elastic fracture mechanics for ductile material failure prediction, the plastic portion of fracture toughness must be excluded. This paper aims to develop a $J$-integral based method for determining the elastic fracture toughness of ductile metal plates with inclined cracks under biaxial loading. The derived elastic fracture toughness is a function of the plate and crack geometry, strain-hardening coefficient, yield strength, fracture toughness, biaxiality ratio, and inclination angle. It is found that an increase in yield strength or relative crack depth, or a decrease in Mode-I fracture toughness, leads to a larger ratio of elastic fracture toughness to total fracture toughness. It is also found that the effect of biaxiality ratio and inclination angle on elastic fracture toughness is highly dependent on total fracture toughness. It can be concluded that the developed model can accurately predict the fracture failure of ductile thin metal structures with inclined cracks under biaxial loading.

The problem of oblique water wave scattering and trapping by a submarine trench in a two-layer fluid is analyzed within the context of the linearized water wave theory. Under the potential flow approach, the solution of the associated boundary value problem is derived by the matched eigenfunction expansion method. Numerical results for the reflection and transmission coefficients in surface and internal waves for several physical parameters are obtained. The reflection and transmission coefficients are computed and analyzed in various configurations. The depth and width of the trench affect the reflection and transmission coefficients in both modes. For a symmetric trench, the periodicity of zero and the minimum reflection values increase as the width of the trench increases. The angle of incidence significantly affects the reflection and transmission coefficients at surface mode. In addition to the structural properties of the submarine trench, wave reflection and transmission in surface and internal modes are strongly dependent on the fluid density ratio and the interface location. The numerical results are compared with cases in the specialized literature and very good agreement is achieved. In order to verify the computational results, energy relations are derived and the numerical results are found to satisfy these relations accurately.

To evaluate an arbitrary multiaxial stress state, the concept of the equivalent stress can be used. Because of its simplicity and clarity, this concept is now widely used in the component design. Many strength criteria based on the equivalent stress concept have been formulated during the last two centuries. Currently, a large number of strength criteria are available. The choice of an appropriate criterion for a particular material is the main challenge in applications. The alternative is the formulation of generalized criteria that contain classical strength hypotheses and are suitable for different materials. The generalized criteria of specific studies are selected in this work to describe experimental data for concrete. The generalized strength criteria contain several material parameters. The application of these criteria requires experimental results under multiaxial stress states in addition to tension, compression, and torsion test data. As an example, experimental data for concrete under plane stress loading are the focus of this study. These data are approximated with the help of the chosen criteria. The recommendations for the application of the generalized criteria are provided.

The time-dependent behavior of architected lightweight cellular solids or foams is important to investigate for various structural applications. In this paper, the authors studied the linear viscoelastic properties of a novel architectured foam based on the mathematically known Schwarz primitive (P) triply periodic minimal surface (TPMS), referred to here as P-foam, in both time and frequency domains. Here, three dimensional (3D) representative volume elements (RVEs) at different relative densities (i.e., the ratio of the foam’s density to the density of its solid counterpart) were generated and studied using the finite-element method. The effective time-dependent response of P-foams as a function of relative density and frequencies is investigated. For the first time, an approach similar to the time-temperature superposition principle (TTSP) was adopted to create the master curve of the observed relative density–dependent mechanical responses in both time and frequency domains. Reduced uniaxial, bulk, and shear stiffness-loss map results suggested that the P-foam possesses the highest bulk response whereas the highest damping can be achieved under uniaxial responses. Depending on the applications and loading conditions, variable-stiffness P-foam dampers can be designed with unique and optimized dynamic mechanical properties. Comparison of the relaxation responses of various generic cellular architectures with P-foam showed that the uniaxial response of P-foam is similar to that of Kelvin foam. However, shear relaxation and bulk responses are higher than simple cubic, body centered cubic, reinforced body centered cubic, and Gibson-Ashby foams. Based on RVE micromechanical simulations, a macroscopic constitutive model is proposed for modeling the viscoelastic behavior of structural systems made of the P-foam.

Monochromatic wave scattering on a submerged horizontal plate over variable topographies is studied analytically based on the modified matched eigenfunction expansion method. Under the assumption of the shallow flow over a slowly varying bottom, an approximate solution of the flow in the inner region bounded by a submerged plate and a plane slope is presented based on the potential flow theory and perturbation method. The analytical solution is validated by existing analytical results and experimental data on flat bottoms. Parameter analysis is carried out for three types of variable topographies. The effects of the bottom profile on wave reflection and wave loads are investigated. It is found that there are significant influences on wave reflection due to uneven bottoms. Smaller maximum reflection coefficient appears in the following cases: larger relative slope heights for simple slopes, larger relative hump heights for humped bottoms, and larger relative hump heights for combined bottoms. Compared with the change of wave reflection coefficient, the shift of wave loads over the three types of variable topography seem not to be significant.

The detection of bifurcation in granular soils is a major concern in geomechanics. Recent advances in geomechanics have highlighted the key role played by the mesoscopic structures composed of grain loops in the stability of granular media. Based on an elementary grain loop pattern, this paper investigates the influence of the microstructure on the bifurcation domain topology at the mesoscopic scale. This study shows that, at the mesoscopic scale, the bifurcation domain cannot be consistently defined in terms of the stress state only. Expressed in a stress-microstructure space, the bifurcation domain becomes invariant with the contact regime, the initial microstructure, and the loading path. It is also shown that the microstructural anisotropy is as determinant as the stress state with respect to the bifurcation domain topology. Finally, the mechanical and volumetric behaviors of the granular assembly are shown to be correlated through a proper microstructural variable.

A model for evaluating the lateral earth pressure distribution for retaining walls as a function of intermediate displacement between the full active and passive states is proposed in this paper. The proposed method can be readily used in practice without prior knowledge of earth pressure measurements. The efficacy of the proposed approach is demonstrated through the comparison of the estimated earth pressure coefficients with the experimental results. The proposed approach is useful in assessing the dependence of correction factors for Rankine’s solutions on the effective friction angle and the magnitude of displacement to account for the prefailure behavior of soil at any intermediate state. Similar to a wall pushing into the retained soil, passive earth pressures are generated around driven piles. The coefficient of earth pressure from the suggested model is coupled with cavity expansion theory to estimate the depth of ground heave induced by pile driving. The results of the proposed approach in estimating the ground heave are compared with the finite-element solutions.

In this paper, three-dimensional dynamic responses of a saturated half-space under arbitrary distributed buried time-harmonic load are investigated through analytical developments. In the development, the linear porous medium model established by de Boer is employed to describe the mechanical behavior of the saturated medium. By virtue of displacement potentials, the field equations are fully decoupled into four independent wave equations, which are then treated with finite Fourier and Hankel transformations. Finally, the solutions of filed variables are obtained via the imposition of boundary as well as interfacial conditions, and thereupon presented in the form of an inverse Hankel transform that in general is evaluated with numerical methods. Examples involving surface, buried patch loads are also presented to validate the solutions and examine the effect of the saturated soil’s permeability coefficient.

An unconditionally stable explicit algorithm with second-order accuracy is proposed in state space. Stability, relative period error, and amplitude decay of the proposed algorithm are studied. It is shown that the proposed algorithm is unconditionally stable for linear systems and nonlinear systems whether the stiffness of the structure is the softening or hardening type. This stability property is appealing because currently, explicit algorithms cannot be unconditionally stable when the stiffness is the hardening type. In addition, the stability and accuracy of the proposed algorithm are demonstrated by several nonlinear numerical examples.

Combining the use of external dampers and crossties as a hybrid system to control unfavorable bridge stay-cable vibrations has been successfully applied on a number of cable-stayed bridges, although knowledge about the mechanics and dynamic behavior of such a system is still limited. In the current paper, a generalized approach is developed for formulating an analytical model of hybrid systems which allows development of an analytical model of a complex hybrid system based on a relatively simple parent system, the analytical model of which either is available in literature or can be more easily derived, and then superpose the effect of the remaining component, which can be either a damper or a crosstie. The validity of the proposed approach is verified using a number of cable systems with various configurations, the characteristic equations of which have been analytically derived in the literature. It will then be applied to a more complex hybrid system with two damped main cables interconnected with a crosstie extended to and anchored on the ground or the bridge deck. The respective impact of the damper and the crosstie on the modal response of a hybrid system will also be discussed. The proposed generalized approach is expected to greatly save modeling effort and provide a convenient and useful tool for evaluating and comparing the effectiveness of different hybrid system layouts in the preliminary design stage.

This paper enhances the available generalized beam theory (GBT) geometrically nonlinear (elastic) formulations by including (1) the whole set of nonlinear membrane strain terms, and (2) the nonlinear bending strain terms. Initially, the main steps involved in the derivation, development, and numerical implementation of the novel/enhanced GBT geometrically nonlinear formulation are presented in detail. Then, after comparing the proposed and available GBT nonlinear formulations, numerical results concerning two illustrative examples are presented and discussed. They make it possible (1) to better understand the concepts and procedures involved, and (2) to assess the relevance of the added nonlinear membrane and bending strain terms. Such results (1) concern a Z-column and a lipped channel beam under uniform stress resultant diagrams and buckling in distortional and local modes, respectively, and (2) comprise several equilibrium paths obtained from approximate or rigorous analyses, relevant displacement profiles, modal participation diagrams, and deformed configurations. For validation, the GBT-based results are compared with values yielded by shell finite-element analyses.

This study presents a Structural Health Monitoring (SHM) framework for assessing the integrity of RC structures subjected to corrosive environmental conditions. The presented framework uses the Polynomial Chaos Kalman Filter (PCKF) for accurate prediction of the stochastic characteristics of the chloride profile in RC structures using real time measurements. The PCKF uses available measurement data of the chloride content at specific locations to update the probabilistic characteristics of the chloride ingress model parameters. These parameters are consequently used to forecast the chloride content profile in RC structures. The work builds on the available literature to quantify the various sources of uncertainty associated with the chloride ingress phenomena. Three long-term experimental data sets are used to assess the efficiency of the presented SHM framework by comparing the framework predictions to real time measurements. The experimental data are also used for sensitivity analysis to highlight the effects of the location and frequency of chloride concentration measurements, as well as the chloride ingress modeling assumptions, on the long-term performance of the SHM framework. The results emphasize the robustness of the presented PCKF approach. PCKF is found able to predict, with reasonable accuracy, the experimental measurements of the chloride content in all data sets.

This paper proposes an extension to Gaussian process regression (GPR) for data sets composed of only a few replicated specimens and displaying a heteroscedastic behavior. Because there are several factors that are out of the control of experimenters, it is often impossible to reproduce identical specimens for a same experiment. Moreover, observations from laboratory experiments typically display a heteroscedastic interspecimen variability. Because experiments and specimen manufacturing are expensive, it is uncommon to have more than three specimens to build a model for the observed responses. The method proposed in this paper uses GPR to predict each tested specimen using a shared prior structure and models the global heteroscedastic behavior by combining observations using conjugate prior distributions. An application of the method to high-performance fiber-reinforced concrete experiments highlights fiber addition benefits for reducing water permeability caused by macrocracks.

Experimental tests were conducted on composite rock-concrete specimens with four roughness profiles to investigate the propagation of interfacial cracks under three-point bending and four-point shear conditions. By measuring the initial fracture loads, various combinations of interfacial stress intensity factors (SIFs) of Modes I and II corresponding to the initial fracture conditions were determined. Based on these results, an expression for classifying the initiation of interfacial cracks in mixed Mode I-II fracture was derived by normalization, which could eliminate the effect of interfacial roughness. Furthermore, a criterion for specifying propagation of the interfacial crack that takes into account nonlinear interfacial characteristics was proposed, which indicated that the crack would start to propagate along the interface when the SIFs caused by the external loads and the cohesive stresses satisfied this criterion. Numerical simulations of the interfacial fracture process were also conducted, introducing the crack propagation criterion to predict load–versus crack mouth opening displacement (P-CMOD) curves. They revealed fairly good agreement with the experimental results. Finally, by combining the criterion for maximum circumferential stress with the proposed criterion for crack propagation, the interfacial crack propagation mode was assessed. The results indicated that, once the initial fracture toughnesses for the rock, the concrete, and the rock-concrete interface from the experimental work were obtained, the propagation of interfacial cracks and the corresponding fracture modes, including nonlinear characteristics of the materials and interface, could be predicted using the method derived in this study.

The high-frequency force balance (HFFB) technique is widely adopted for the assessment of wind loads acting on a tall building because of its simplicity and versatility. Although a number of HFFB-based analysis methods have been proposed to predict wind-induced dynamic responses of a tall building, these methods or models have mostly been developed based on various assumptions, which introduce different levels of inherent uncertainties and lead to a practical problem of method and model selections among available HFFB-based methods. It is necessary to quantify uncertainties in selecting the most robust and reliable model to carry out wind-induced response analysis with minimum uncertainties. The novel contribution of this paper is to establish a probabilistic framework for quantifying the model-selection uncertainty and weighting up the superiority among the candidate HFFB-based analysis models. A practical complex tall building is employed to demonstrate the proposed technique of uncertainty quantification in HFFB-based analysis for predicting wind-induced responses. Furthermore, the synchronous multipressure sensing system (SMPSS) test has been conducted in the wind tunnel to provide the benchmark results of the wind loads and a virtual set of HFFB base reactions obtained through integration of the measured pressure field.

Wind-induced internal pressure arising from door or window failure during severe wind conditions has been studied extensively. Most previous studies focus on the cases of openings in the wall, but little attention has been paid to the internal pressure responses of a building with a dominant opening on the roof, although this situation appears frequently due to wind-induced damage or functional use. This paper examines the internal pressure characteristics produced by wind action through a dominant opening on a hemi-ellipsoidal roof and investigates its potential influence factors, including opening sizes, locations, internal volume, and ambient interference. An opening in the wall was also studied and compared with the case having the same size opening on the roof. The study shows that internal pressures were basically negative under roof opening cases but might become positive at several wind azimuths when there is an interfering building nearby. Spectra of internal pressures contained two resonance peaks, which corresponded to Helmholtz resonance and vortex shedding, respectively, and varied significantly with wind directions. Due to the coupling effect of vortex shedding, the classical Helmholtz frequency equation, and the current volume adjustment method to maintain frequency similarity between full-scale and model-scale might be unsuitable for roof opening cases. Reducing the internal volume increased the standard deviation of internal pressure, but had an insignificant effect on its mean values. Compared with the roof opening case, wind actions through an opening in the wall would generate worse net suctions on the roof but lead to a smaller Helmholtz resonance frequency. Roof failure resulted in larger maximum internal suctions than wall failure and was thus more dangerous to the windward wall bearing positive external pressures. Internal pressure responses controlled by Helmholtz resonance could be deemed as a quasi-Gaussian processes. The ambient interferences could affect Gaussian characteristics of internal pressures.

This research discusses the design, modal analysis, and additive manufacturing of a hexakis icosahedron frame for use in a vacuum lighter-than-air vehicle (VLTAV). A frame in the shape of a hexakis icosahedron, when encased by a thin membrane-like skin, would be able to withstand the pressure load induced by internal air evacuation and produce positive buoyancy. For a better appreciation of the force resistance within the hexakis frame, a manufactured frame was constructed. The actual frame has many varying oriented beams, making its construction complicated for standard production methods. Therefore, additive manufacturing was incorporated. A portion of this paper is directed toward the description of the method carried out. A 0.1778-m-diameter hexakis icosahedron frame was additively manufactured using VeroWhitePlus plastic. A modal experiment using a laser vibrometer was performed in order to determine the eigenvalues of the structure for comparison to the modal analysis results of a finite element (FE) model of the frame assuming a free-free boundary condition. This comparison allowed for the verification of the equivalent modulus of elasticity used in an analysis and the overall construction of the model. The finite element model predicted the first two frequency modes within 1% of the experimental results. Because the FE model accurately predicted the dynamic properties of the frame, the modeling technique in which the assumed member connections were verified led to confidence for future modeling.

To model the displacement field of asymmetric one-dimensional structural elements, in which a transverse-bending motion couples with axial motion, a formulation with five displacement components is developed. The proposed formulation extends Timoshenko beam theory to asymmetric cases and adds two displacement components to estimate in-plane warping. Via Hamilton’s principle, the coupled partial differential equations that govern the components of the displacement field together with the corresponding boundary conditions are derived. To validate the formulation, the lower natural frequencies of several case studies, including a monolith of Koyna Dam in India, are computed and compared with those given by two-dimensional finite-element models. To analyze the examples through the proposed formulation, standard finite-element analysis of one-dimensional elements with five displacement components is applied. In all cases, results from the proposed plane stress formulation proved to be in very good agreement with those provided by two-dimensional models.

In this study, a mathematical model for the Reynolds stress profiles in different regions of a submerged turbulent plane offset jet was developed. The two-dimensional Reynolds-averaged Navier-Stokes and the continuity equations were solved for the determination of the velocity and the Reynolds stress profiles within the jet layer in different regions of a submerged offset jet. The theoretical derivations involved a boundary layer approximation. The velocity profiles in the preattachment region obeyed an exponential function, whereas those in the impingement and wall jet regions followed a combination of a power function for the inner layer and an exponential function for the outer layer of the jet. The computed velocity and the Reynolds stress profiles corresponded well with the previous experimental results of the flow in submerged turbulent plane offset jets.