Journal of Engineering Mechanics

The main objective of this study was to quantify effect of fibers on the onset of strain localization in elastic-plastic cementitious composites. To this end, multidirectional fibers were embedded into an elastic-plastic cementitious matrix and the resulting composite was described by several different types of nonassociated Drucker-Prager hardening plasticity models. Diagnostic strain localization analyses were conducted, thus providing strain and stress levels at the onset of strain localization, along with corresponding directions and modes of strain localization. Several actual uniaxial tension and compression tests on plain cementitious composites and on high-performance steel fiber-reinforced cementitious composites were investigated. Results showed that the onset of strain localization was slightly delayed in uniaxial tension and more significantly delayed in uniaxial compression tests on high-performance fiber-reinforced cementitious composites as compared to the plain mortar. Specifically, the diagnostic strain localization analysis appears to detect the inception of a fiber-induced distributed cracking in uniaxial tension tests, and the onset of a fiber-induced delay of a major crack localization in a uniaxial compression test.

Dispersion occurs when a wave propagates through a heterogeneous medium. Such a phenomenon becomes more pronounced when the smallest wavelength of the incoming pulse approaches the size of a unit cell, as well as when the contrast in mechanical impedance of the constituent materials increases. In this contribution focusing on periodic bilaminate composites, the authors seek an accurate description of the wave propagation behavior without the explicit representation of the underlying constituent materials. To this end, a gradient elasticity model based on a novel homogenization strategy is proposed. The intrinsic parameters characterizing the microinertia effect and nonlocal interactions are fully quantified in terms of the constituent materials’ properties and volume fractions. The framework starts with suitable kinematic decompositions within a unit cell. The Hill-Mandel condition is next applied to translate the energy statements from micro to macro. The governing equation of motion and traction definitions are next extracted naturally at the macrolevel via Hamilton’s principle. The ensuing fourth-order governing equation of motion has the same form as a reference gradient model in the literature, which was derived through a fundamentally different homogenization scheme. The predictive capability of the proposed model is demonstrated through four examples, with bilaminate composites encompassing a comprehensive range of material properties and volume fractions. It is furthermore shown that the proposed model performs better than the reference model for bilaminate composites with low to moderate contrast in mechanical impedances.

The working characteristics of targeted surface sensing systems—such as fluid velocity and concentration limits—have mostly been explored through experimental trials. Here we develop a novel scaled collision theory to facilitate the experimental screening process in determining the optimal system parameters specific to sensing discrete molecular or particulate targets with low concentration in a bulk fluid system, such as biomarkers, pollutants, or explosives. A simple fluid sensor system was developed and subjected to steady-state Couette flow to explore key parameters. Validated by 177 particle-based coarse-grain simulations, this theory indicates that the chance of successful pairing events between molecular markers and its corresponding targets—or hits—is determined by their concentrations, binding affinity or energy, and more importantly the flow velocity. Scaled collision theory reveals great potential to be used as a system design tool for a wide spectrum of sensing applications, ranging from water and air quality monitoring to biomedical detection and disease diagnostics.

A wave power device comprising a floating circular buoy on the water surface and a submerged cylinder on the sea floor has been proposed in previous studies. This paper considers the wave interaction with a stationary wave power device of this kind and investigates the second-order hydrodynamic interaction between the buoy and the caisson. To achieve this, the first-order wave diffraction problem was first solved based on the eigenfunction expansion method. Then a semianalytical solution for the second-order double-frequency wave force applied on the buoy was developed based on the indirect method. After conducting convergence tests, the results from the present method were compared with those from the direct method and the higher-order boundary-element method (HOBEM) and good agreements were obtained. Then calculations were performed for different sizes of the caisson. The contribution of each constituent component to the whole second-order double-frequency wave force was investigated and the effects of the caisson size on the hydrodynamic loads experienced by the buoy are discussed.

Models are used to represent and characterize physical phenomena. When there are many plausible models for a particular phenomenon, the modeler can exploit the computational tool called model falsification to systematically eliminate models that do not reasonably fit measured data. Model falsification typically compares measurements and their predictions by different models, and rejects a model if some metric of the difference between them is outside some prescribed bounds. This paper compares two model falsification approaches: a conventional bounds on residual errors and a proposed bounds on a model’s prediction of the likelihood of the residual errors. The bounds in both approaches are selected based on two error control criteria: the more commonly used familywise error rate (FWER) and—proposed herein for model falsification—the false discovery rate (FDR). Because FDR control significantly increases the likelihood of rejecting an invalid model when there are many measurements, FDR provides advantages over FWER in exploratory studies. A variant of the second approach, using likelihood bounds specified by a constant probability mass contained within those bounds, is also investigated. Unlike many model falsification studies, the focus herein is on systems with many measurements, spread across spatial and/or temporal dimensions, such as dynamical systems. An elementary example is used to show the principles of each approach. A second example considers a series of four-degree-of-freedom models of a structure subjected to an earthquake excitation. The results from these examples show that FDR does indeed increase the number of falsified models, whereas the use of likelihood bounds additionally gives unfalsified models confidence values, which can also be used for maximum likelihood parameter estimation.

This paper introduces a novel approach based on dimensional analysis for designing explicit displacement algorithms for use in analyzing nonlinear structural dynamics problems. Using this approach, a one-parameter family of three-step unconditionally stable explicit displacement algorithms with controllable numerical energy dissipation, the CQ-3 method, is developed. The proposed method is promising for solving nonlinear structural dynamics problems with its properties of unconditional stability; explicit formulations of both displacement and velocity; controllable numerical dissipation; second-order time accuracy for displacement, velocity, and acceleration; one solver within one time step; and no overshoot for both displacement and velocity. Numerical examples are presented to demonstrate the potential of the proposed method.

The frequency response function governs many important processes. Defined as the quotients of the fast Fourier transform coefficients, frequency response functions can be modeled as ratio random variables in the complex domain. The circularly symmetric complex normal ratio distribution proposed previously is restricted to quantifying the uncertainties for the quotients of complex Gaussian random variables with zero mean. Such limitation motivates research to enlarge the group of probability distributions, allowing a wider scope of applicability. This study provides a theoretical proof for the closed-form of a generalized proper complex Gaussian ratio distribution using the principle of probability density transformation in tandem with an advanced integral technique. The equivalence between the distribution properties of complex ratio random variables and their counterparts in the real-valued domain is also proven. The generalized proper complex Gaussian ratio distribution is then used to infer the statistics of frequency response functions. Stochastic simulation and experimental study are used to demonstrate the goodness and efficiency of the proposed probabilistic model.

A methodology has been developed to account for the elastic–adhesive interface effect on the effective elastic moduli of fiber-reinforced asphalt concrete. To consider the large deformation of asphalt mixtures, the nonlinear factor related to the second-order term of strain was first proposed. The effective medium method was introduced to obtain the closed form for the elastic moduli of isotropic asphalt concrete reinforced by unidirectional isotropic fibers of a circular cross section. The elastic and adhesive coefficients were used to describe the interface effect. To reveal the influence of interface microstructure in asphalt concrete quantitatively, some numerical examples are given. It was found that the effective elastic moduli showed significant variation with the interface microstructure in asphalt concrete, especially with the small radius of fibers. The interface effect with a large deformation of asphalt concrete was also examined in detail.

A solution algorithm is proposed for nonlinear structural analysis problems involving static and/or dynamic loads based on the Lyapunov stability theory. The main idea is to reformulate the equations of motion into a hypothetical dynamical system characterized by a set of ordinary differential equations, whose equilibrium points represent the solutions of the nonlinear structural problems. Starting from the Lyapunov stability theory, it is demonstrated theoretically that this hypothetical dynamical system is characterized by a global convergence to the equilibrium points for structural dynamics, i.e., the convergence is guaranteed independently of the selection of the initial guess. This feature overcomes the inherent limitations of the traditional iterative minimization algorithms and relaxes the restriction on the selection of the initial guess for various structural nonlinear behaviors. The validation of implementing the algorithm is demonstrated using a geometrically nonlinear pendulum problem with a closed-form exact solution. Moreover, comparisons between the proposed algorithm and Newton-Raphson type algorithms are presented using several numerical examples from structural statics and dynamics. Finally, the scalability of the proposed Lyapunov-based algorithm is discussed via adaptive switching of nonlinear solution algorithms at the problematic time steps.

This paper develops an algorithm for generating the three-dimensional (3D) heterogeneous microstructure of asphalt concrete based on random modeling. The asphalt concrete was modeled as heterogeneous material with fine aggregate matrix (FAM), coarse aggregates, and air voids. We generated 3D aggregate shapes with three two-dimensional (2D) projections randomly selected from the aggregate image database. We generated the 3D models of asphalt concrete by randomly placing 3D aggregates and air voids into the virtual specimen with compact packing. We predicted the dynamic modulus of asphalt concrete specimens with different microstructures through finite element (FE) analysis and validated with experimental data. The relative differences between the average dynamic modulus and the experimental data ranged from 0.32 to 6.01% for different frequencies, which indicates that the 3D heterogeneous microstructure model is acceptably accurate. The volume of aggregate in each sieve is the major factor controlling bulk material properties like dynamic modulus. We also generated 2D heterogeneous models of asphalt concrete by cutting the 3D model from different cross sections. The variation of dynamic modulus with the 2D models was much greater than the variation with the 3D models. The ratio of coarse aggregate content in the 2D and 3D models can range from 0.86 to 1.35. Although, in general, the predicted dynamic modulus increases as coarse aggregate content increases in 2D models, we observed variations due to differences in microstructure.

Hysteresis is a highly nonlinear phenomenon, which is observed in different branches of sciences. The behavior of the hysteretic systems is usually controlled by some nonmeasurable internal states. It makes hysteresis be a nonunique nonlinearity, and therefore hysteresis identification is a cumbersome task. In this paper, which uses the capability of the least-squares support vector machine (LS-SVM) in static function approximation, a new rate-dependent hysteresis model is proposed. First, the model converts the hysteresis’ nonunique nonlinearity into a one-to-one mapping by means of classical hysteresis operators. Second, the mapping is learned by an LS-SVM. The training algorithm of the model is introduced and how the model can be applied in different situations is discussed. The proposed model is assessed with different hystereses with different properties. The generalization capability of the proposed model is compared with a neural-based hysteresis model. Finally, the application of the proposal is investigated in the feed-forward control of the hysteretic systems with an example. The results show the high accuracy of the proposed model in hysteresis simulation and control even for the experimental data.

Compared to the seismic motions recorded on the onshore sites, the quantity of offshore earthquake recordings is very limited. This paper presents a novel method to simulate spatially varying ground motions at multiple seafloor sites by using the more abundant onshore earthquake records. A pair of onshore and offshore seismic motions recorded in the same earthquake event is selected, and the onshore recording is employed as the predefined motion to simulate offshore seismic motions. The detailed information of the onshore and offshore sites beneath respective stations is collected, and the ground motion transfer functions are computed by including the effects of seawater and soil saturation on the seismic P wave propagation. Using the power spectral density (PSD) functions of the onshore recording and the onshore and offshore site transfer functions, the ground motion PSD functions on the offshore site are estimated, and the three-component seafloor seismic motions are synthesized. The basic characteristics of the synthesized seafloor motions are compared with the seafloor recording, and the feasibility of the proposed method is validated. Finally, the approach is further extended to the simulation of spatially varying seafloor motions by considering the spatial variation between the seafloor motions at various offshore sites. The effect of local offshore site on the lagged coherency of spatial seafloor motions is also investigated.

This paper investigates the axisymmetric free vibrations of annular single-layered graphene sheets with different boundary conditions using nonlocal elasticity theory. The analysis procedure is based on the first-order shear deformation theory and small deflections assumption to derive the equations of motion which are a system of partial differential equations with variable coefficients. In order to determine the transverse natural frequencies as well as the radial natural frequencies analytically, the perturbation technique is applied to solve these equations. The transverse natural frequencies are calculated using classical plate theory. The results of both theories are compared with those obtained from the literature. A parametric study is performed and the effects of nonlocal parameter, geometry, and boundary conditions on the natural frequencies are investigated.

Fragility functions indicate the probability of a system exceeding certain damage states given some appropriate measures that characterize recorded or simulated data series. Presented in two main parts, this paper develops fragility functions in their utmost generality, accounting for both (1) multivariate intensity measures with multiple damage states and (2) longitudinal damage state dependencies in time. Without adopting the limiting assumption of common variance to avoid improper function crossings, the first part presents what is here compactly termed as extended fragility functions. As shown, these are best supported by the softmax function for any arbitrary distribution of the exponential family to which the intensity measures of different states may belong, including the typically used normal distribution in the logarithmic scale of intensity measures. In the second part, generalized fragility functions are introduced for cases where multiple system state transitions need to be captured. To that end, dependent Markov and hidden Markov models are employed because they are able to portray longitudinal data dependencies and reveal intrinsic deterioration trends for multiple sequential events. Numerical results are presented, together with underlying implementation details, statistical properties, and practical suggestions.

How to detect the prestress loss of the bridge in a fast and economical way is still a challenging problem for bridge engineers. Although some sensors have been developed to monitor the prestress, it is usually difficult and expensive to install, maintain, and monitor these sensors. Drive-by inspection, using vehicle response to identify the prestress loss, could be a good alternative. In this paper, an earlier-developed prestressed bridge vehicle interaction model has been modified to account for the influence of effective rigidity and the gravity load. Both half and quarter vehicle models were adopted in the study. Numerical simulations were conducted to show that light, low-frequency vehicles moving at low speeds have a better performance in detecting the bridge prestress loss than the heavy, high-frequency vehicles with high speeds. Also, the maximum vertical acceleration of vehicles could correlate with the prestress loss very well.

The need to reconstruct moving acoustic sources arises in many real-world applications—for example, smart highways for detecting the motions and weights of vehicles, and underwater acoustic forensics. Despite the usefulness of acoustic source inversion (ASI), to date, few papers have shown the feasibility of identifying unknown signal amplitudes and time-varying positions of moving acoustic sources of an arbitrary number within or on complex media without any prior knowledge about the sources. To fill this gap, this paper introduces a new computational framework for reconstructing spatial and temporal profiles of moving acoustic sources from wave responses measured at sparsely distributed sensors. To reconstruct acoustic source profiles without a priori knowledge of the sources, the presented ASI method employs discretization of source functions in space and time. The value of each discretized parameter is estimated at every iteration in the inversion procedure. Because of the high resolution of the discretization, the number of inversion parameters ranges in the hundreds of thousands in the presented numerical examples. To tackle such a large-scale inverse problem, a state-adjoint-control-equation-based optimization technique is employed. The finite-element method (FEM) is used to obtain wave responses in state and adjoint problems. Numerical experiments, in one-dimensional (1D) undamped heterogeneous solids, prove the robustness of this method by reconstructing spatial and temporal profiles, i.e., speeds, locations, frequencies, and magnitudes, of multiple dynamic moving loads. The accuracy of convergence toward the target in the numerical examples is excellent, reconstructing the spatial and temporal footprints of the sources.

In the present work, the variable negative stiffness device (VNSD) is presented for seismic protection through apparent weakening. Equations relating the force-displacement behavior for two different VNSD configurations are presented, and a parameter search is conducted to identify the system parameters leading to three different desired force-displacement profiles. Validation of the concept is provided through laboratory testing on a small-scale prototype subject to cyclic loading. Then, numerical simulations are performed for an inelastic building model with supplemental damping and three different VNSD systems subject to a suite of earthquake ground motions. The results show that the performance of the VNSD systems with and without stiffening was the same for the structure without yielding, and comparable when the structure experienced severe yielding. For the structure subject to extreme yielding, significantly larger peak displacements and smaller peak absolute accelerations and base shears were obtained for the VNSD system without stiffening. Finally, the effect of increasing supplemental damping in the structure on the performance of the VNSD systems was investigated.

A semianalytical method is developed to obtain the dynamic response of laterally loaded piles in a multilayered soil. In the analysis, the soil is modeled as a three-dimensional viscoelastic continuum with frequency-independent hysteretic material damping and the pile as a circular elastic Timoshenko beam. Unlike the Euler-Bernoulli beam that is conventionally used to model laterally loaded piles in various analytical, semianalytical, and numerical studies, the Timoshenko beam theory accounts for the effect of shear deformation and rotatory inertia within the pile cross-section that might be important for modeling short stubby piles with solid or hollow cross-sections and piles subjected to high frequency of loading. In the analysis, the soil displacements in the horizontal direction are expressed as products of separable functions, and the extended Hamilton’s principle in conjunction with the calculus of variations is used to obtain two sets of coupled differential equations governing pile and soil motions along with the relevant boundary conditions. The coupled equations are solved analytically and numerically following an iterative algorithm. The differential equation and boundary conditions governing pile motion are progressively reduced to model the pile as a Rayleigh beam and a Euler-Bernoulli beam; thus, a unified framework incorporating various beam theories for the dynamic soil-structure interaction of laterally loaded piles in a multilayered soil is developed. The accuracy of the present analysis is verified against the results of several analytical and numerical solutions available in the literature. It is shown from the solved example problems that rotatory inertia has practically no effect on the dynamic response of piles, whereas there is some effect of shear deformation on the response of piles with hollow cross-sections.

This paper investigates the evolution of the fabric for different contact networks (i.e., the strong, weak, and overall contact networks) in granular material. Two-dimensional tests along proportional strain paths and simple shear tests are conducted using the discrete element method (DEM). Results show that the coaxiality between the principal directions of the fabric tensor for the overall contact network and that of the stress tensor depends on the loading conditions. The principal direction of the fabric tensor for the strong subnetwork is always coaxial with the stress direction. In addition, the major principal direction of the fabric tensor for the strong subnetwork is perpendicular to that of the weak subnetwork, regardless of any principal stress rotation. The fabric tensor for the strong subnetwork and the stress tensor at the critical state are proportional, with the coefficient of the proportionality being a function of the mean stress, if the critical stress can be approached.

Evaluating the mean-square response at the transient state of a single degree of freedom (SDOF) system to stationary random excitation has been extensively studied in the past, but the explicit closed-form solution has not been available unless the excitation was considered to be a physically unrealizable white noise process. In this paper, explicit closed-form solutions for the mean-square response are derived for arbitrary input power spectral density (psd) functions. While all existing solution methods for evaluating the mean-square response have always been conducted in the time and/or frequency domains, the proposed method is operated in the complex plane (Laplace domain) based on pole-residue formulations. Not only is the proposed approach is much more efficient than other existing approaches, but also meaningful physical and mathematical insights can be gained in its solution procedure. To demonstrate the procedure, this paper considers the excitation process characterized by a white and nonwhite psd, respectively, and the corresponding closed-form solutions for the transient mean-square response of SDOF systems are derived. The correctness of the closed-form solution for the nonwhite psd is verified by Monte Carlo simulations.

In this article, the eigenfrequency responses of a nanoplate structure are evaluated numerically via a novel higher-order mathematical model and finite-element method including nonlocal elasticity theory. A new computer program has been prepared based on the present model to compute the frequencies of the nanoplate structure. The accuracy of the numerical solutions has been checked through proper convergence and comparison with available published data by evaluating an adequate number of examples. The conclusions related to the capability of solving nanoplate structural problem and subsequent accuracy of the current higher-order finite-element model have been demonstrated by solving several illustrations. Also, the numerical examples are solved by considering the nonlocal elasticity as well as the scale effect and other geometrical and material parameters (aspect ratio, size, and nonlocal parameter) that may directly affect the final solutions are discussed.

An analytical solution for groundwater flow through a circular tunnel in anisotropic soils is derived based on conformal mapping and can be used to calculate the water flow rate into the tunnel and predict the pore water pressure distribution in surrounding soils. If the vertical and horizontal permeabilities are equal, this analytical solution is reduced to the solution for the isotropic flow condition. This proposed analytical solution is verified by numerical simulations. The water flow rate into the tunnel decreases with a decreasing value of soil permeability in the horizontal direction, and the pore water pressure distribution is distorted due to the anisotropy of soil. This proposed analytical solution provides an efficient approach for estimating the groundwater inflow into a circular tunnel accounting for anisotropic soils.

The nonlinear dynamic characteristics of rectangular and cylindrical tuned liquid dampers (TLDs) were studied by the so-called regularized boundary integral method (RBIM). An artificial damping coefficient was also included to simulate the energy dissipation of liquid sloshing. The effect of the nonlinear liquid sloshing of a TLD on the response of a single-degree-of-freedom (SDOF) system called the RBIM model in this paper was especially emphasized and intensively investigated. The equivalent tuned mass damper (ETMD) model based on the linear sloshing assumption was also employed for comparison and preliminary design of TLD. The numerical results of rectangular and cylindrical TLD examples by RBIM model compared with that by ETMD model or the experimental ones were included. Generally, the RBIM model can successfully predict the effect of the nonlinear liquid sloshing on a TLD’s performance.