Journal of Engineering Mechanics

In this paper, we establish a coupled damage-plastic constitutive model in the scheme of small deformation assumption, based on a continuum damage mechanics model proposed by Lemaitre, for the thin-walled circular steel tubes widely used in space structures. First, a new damage evolution law is developed for steel tubes. Then the isotropic damage-plastic constitutive model is created within the thermodynamics framework. In addition, the numerical integration algorithm for the proposed model is formulated based on the well-established operator split methodology and is implemented into ANSYS through the user-defined material subroutines. The uniaxial tension test and the spatial hysteresis experiment for thin-walled circular steel tubes are performed, which serves as calibration conditions for the new proposition. The model parameters are determined by the inverse optimization method and the least squares fitting method. Numerical results obtained from the proposed and Lemaitre model are compared with experimental data obtained by spatial hysteresis, and the predictive ability of both models is discussed in terms of the force-displacement hysteretic curves, the initiation and propagation of fracture, and the evolution of the damage variable. It is illustrated that the established model presents a good agreement with experimental observation. Furthermore, it performs a better prediction compared to Lemaitre’s model. Lemaitre’s model is able to predict the correct location for fracture onset but fails to capture the potential path of fracture propagation and the displacement at the fracture.

A train–rail–bridge (TRB) interaction model of vector mechanics (VM) is developed to predict the derailment of a train traveling over cable-supported bridges under crosswinds. The aerodynamic coefficients measured from the bridge section-model in wind tunnel testing is used to simulate the unsteady wind pressure acting on the train-bridge system by buffeting forces in the time domain. A versatile wheel-rail contact model considering the wheel-rail contact geometry is then formulated to assess the risk of derailment of a running train. The feasibility and effectiveness of the proposed VM-TRB model are verified by comparison with a conventional finite element procedure. To assess the running safety of the train, a two-phase plot of derailment factors for each pair of wheelsets is generated. The plots indicate that both wind velocity and train speed are critical factors that lead the train cars to potential derailment. Nevertheless, the linking railcar couplers play a holding role in reducing the separation or jumping of the moving wheels from the rail. The case study well demonstrates the capability of the VM-TRB model in dealing with train derailment.

This study evaluates sediment gradation effects on clear-water scour at bridge piers. By considering the average erosion and deposition rates in a pier-scour hole, the normalized equilibrium scour depth is theoretically shown to be a cubic function of the densimetric Froude number. Comparisons with experimental data demonstrate that the cubic law achieves its best fit when the representative particle size is taken to be $d_{84}$. The present prediction equation, which is founded on rational theoretical principles, provides an improved approach to evaluating sediment gradation effects on clear-water scour around bridge piers apart for pure empiricism.

In this paper, the sparse Bayesian learning (SBL) approach previously proposed for the characterization of one-dimensional (1D) soil spatial variability is extended to a more realistic three-dimensional (3D) setting. Direct extension is not computationally feasible because of significant runtime associated with inverting very large matrices and errors associated with computing their determinants. Based on the separability assumption in the autocorrelation function, the current paper successfully extends the SBL to 3D that is computable in practice. The numerical errors associated with large matrices are also mitigated. The second contribution of the current paper is a new efficient method of simulating conditional random fields in 3D based on a dense-lattice assumption. The analysis results for two real case histories show that it is now computationally feasible to characterize the statistical uncertainties in the autocorrelation parameters and trend function as well as to simulate conditional random field samples for 3D problems using the proposed method. To our knowledge, this is the first time we achieve realism in probabilistic site characterization and practicality in runtime at the same time.

Galloping of iced conductors is a kind of self-excited aeroelastic vibration at low frequency and large amplitude causing various damage to transmission tower-line systems. This paper proposes viscoelastic-damping interphase spacers (IPSs) for reducing or mitigating galloping of multiphase transmission lines. Equations of galloping motion are established for a simplified model of two-phase conductors connected by viscoelastic-damping IPS. The multiple-scale method (MSM) is then used to derive an analytical solution of the galloping amplitude with validation from both the finite-element method (FEM) and numerical solutions. Based on analytical solutions, the effects of structural dynamic parameters of conductors and viscoelastic-damping IPSs on galloping critical wind conditions and galloping amplitudes are investigated in a parametric space as well as in the consideration of transmission engineering practice. It is found that there exists an optimal damping ratio of viscoelastic-damping IPSs to achieve the maximum critical wind speed of galloping for the two-phase conductor system. The antigalloping effect of an IPS is largely dependent on the frequency ratio of a two-phase conductor as well as the relative stiffness of IPSs.

This paper presents the dynamic analysis of structural systems using the homotopy perturbation method (HPM). HPM was applied to the first-order differential equations of motion defined by the state vector. This approach is in the framework of time-history matrix analyses. According to the formulas obtained from HPM, response of the system was achieved by sequential product of the characteristic matrix of the system. This method was theoretically compared with the exponential matrix method (EMM). Based on the obtained formulas, nonlinear structural analysis was performed in addition to the linear method. The applicability and efficiency of the proposed method were tested with the classical and nonclassical damping structures and with different dynamic behaviors. Solutions of this method were compared with solutions of EMM and the time-integration method (TIM). The results of the proposed method were in good agreement with those of the two other methods in linear and nonlinear analyses.

Fractional derivatives, owing to their nonlocal behavior, are well suited for modeling the fate of contaminants in a heterogeneous medium. This study develops the mathematical formulation and the solution of a one-dimensional (1D) fractional flux advection-dispersion equation (FFADE) for an increasing or decreasing nonlinear source of contamination in the permeable region. In the proposed model, the first-order space derivative is replaced with the fractional derivative of order ($\alpha -1$) ($1<\alpha <2$) in a Riemann-Liouville sense. The model assumes a spatiotemporally varying dispersion and seepage velocity, constant dispersion and uniform seepage velocity, linear dispersion and linear seepage velocity, and quadratic dispersion and linear seepage velocity, exhibiting various levels of medium heterogeneity. Initially, the medium is considered to be polluted with solute concentration $c_0$ and spatially varying specific concentration $c_i$. The approximate solution to the model is obtained by the modified Adomian decomposition method. It is remarked that change in the medium’s heterogeneity alters the peak of solute concentration, and the presence or absence of advection in the solute transport process significantly affects the concentration distribution. The obtained results are validated with field data available in the literature. The obtained solutions may be used to predict solute concentration in the permeable region from penetrating contaminant sources situated at any place along a vertical plane perpendicular to the direction of, for example, groundwater flow.

Clay minerals are platelike particles that play a critical role in problems involving swelling, deformation, and failure. Fundamental understanding of these phenomena and the parameters that influence them requires studies at the nanoscale. The nanoscale mechanism of the sliding of clay sheets at different states of hydration and hydrostatic stress was studied here using molecular dynamics in an isobaric–isothermal ensemble. The hydration state lay in the range of crystalline swelling ($0–400{\mathrm{mg}}_{\mathrm{water}}/{\mathrm{g}}_{\mathrm{clay}}$), and the hydrostatic pressure was varied in the range 5–12 GPa. Under hydrostatic pressures as high as several gigpascals, the mobility and the molecular structure of water are comparable to those of supercooled water. Despite high hydrostatic stresses, the failure was located in the shear-dominated zone. Examination of the molecular structure of interlayer water, number of hydrogen bonds, and their configuration during shear loading showed evidence of stick-slip phenomena similar to those found in thin films. The number of hydrogen bonds between interlayer water molecules increased as the clay–water system approached the slip point. Hydration state and hydrostatic stress influenced the stress–strain behavior of system and the average shear stress. The hydration states, in which the maximum average shear stresses occurred, coincided with the formation of the second, third, and fifth water layers. The shear strength decreased with the increase of water content above $340{\mathrm{mg}}_{\mathrm{water}}/{\mathrm{g}}_{\mathrm{clay}}$. The nanoscale cohesion and friction angle of the layers were calculated using the Mohr–Coulomb failure criterion and were found to be in good agreement with previous studies.

The sloshing phenomenon in an impervious rectangular and cylindrical tank filled with a porous medium is investigated in this article. Based on linear wave theory and Darcy’s law, the supplementary solutions of transient and steady-state motions can be solved. An equivalent mechanical system that accounts for the sloshing damping due to the porous medium is then established from a structural dynamics point of view. The model has the same kinetic energy, sloshing force, and overturning moment during excitation as actual flow. Therefore, dynamic equivalence can be guaranteed. The dynamic characteristics and modal responses of the liquid in the rectangular and cylindrical tanks are investigated. The analytical method is verified by an impulsive-excitation experiment. In this experiment, a linear wave response is observed, and the sloshing frequency and damping ratio are confirmed. The analytical method can predict the main characteristics of this flow regime very well.

An integral-type nonlocal elastoplasticity model is proposed and formulated in a one-dimensional scenario to address the strain-softening problem. This nonlocal model includes not only the nonlocal plasticity but also the nonlocal elasticity. The resulting elastic constitutive equation and the plastic consistency condition are ill-posed Fredholm integral equations of the first kind whose solutions are instable without appropriate regularization. In this paper, the Tikhonov-Phillips regularization method is used to reformulate the integral-differential consistency condition to obtain an approximate solution of the local internal variable, which is stable and smooth. A detailed parametric study is carried out to examine the influences of the regularization parameter, the internal length scale, the plastic modulus ratio, and the tolerance of the nonlocal yield condition on the regularized solutions. A numerical example shows that the solutions from the proposed model and the regularization method are mesh-independent. A comparison of the results from the proposed model with those from the nonlocal plasticity model and from the gradient-dependent plasticity model shows good agreement.