Journal of Engineering Mechanics

Pressure solution involves mass transfer by dissolution, diffusion, and precipitation in pores or at grain interfaces, which may result in mechanical healing. Dislocation glide is another deformation mechanism that plays a significant role in the behavior of polycrystals. In this paper, we use Eshelby’s self-consistent homogenization scheme with imperfect interfaces to calculate the macroscopic mechanical and diffusive properties of an elasto-viscoplastic porous composite made of imperfectly bonded crystals. Using halite as a model material, the proposed self-consistent model is calibrated and verified against published results of experimental creep tests. Simulations highlight that healing by grain boundary precipitation (by contrast with in-pore precipitation) is a limiting factor for pressure solution, because healed interfaces have lower diffusivity than fluid-filled interfaces. The homogenization approach provides an explanatory framework for the lower creep deformation observed for larger grains, and forecasts lower diffusivity for smaller grains. Sensitivity analyses show that grain boundary healing decelerates specimen compaction, while precipitation in the pores controls the evolution of effective diffusivity.

Abstract

This study presents results from cyclic testing on various configurations of a recently developed pressurized sand damper in which a steel sphere is moving within a cylindrical tube filled with sand that is under pressure. The experimental campaign investigated the effects of the key design parameters of the damper, namely, the effect of the clearance between the moving sphere and the cylindrical tube and the effect of the overall length of the damper to its force output. The recorded force–displacement loops when normalized to the strength of the pressurized sand damper reveal remarkable order with stable behavior and confirm that the force output is nearly rate-independent. The paper also presents recorded force–displacement loops where the sphere mounted on the piston rod is replaced with a bolt where only the bolt head and nut are protruding from the moving piston rod. With this configuration, the pinching behavior of the pressurized sand damper at longer strokes is suppressed without generating large forces at longer strokes.

Practical Applications

The increasing need for structures to meet acceptable performance levels during earthquake and wind excitation has led to the development of various high-performance design and retrofit strategies. Supplemental damping is a widely accepted response-modification strategy for structures where energy is dissipated in dedicated, specially designed energy dissipation devices. Motivated by the recent failures and displacement limitations of existing energy dissipation devices, this paper examines the behavior of an innovative, reliable, long-stroke, low-cost energy dissipation device in which a steel sphere is moving within a cylindrical tube filled with sand that is under pressure. One of the novel aspects of the proposed pressurized sand damper is that it dissipates energy through the hysteretic behavior of sand that can be enhanced by controlling the externally exerted pressure on the sand. The experimental campaign investigates the effects of the key design parameters of the damper, namely, the effect of the clearance between the moving sphere and the cylindrical tube in association with the effect of the overall length of the damper to its force output.

Abstract

The aim of this paper is to explore the mechanical characteristics of lattice-based airless tires made by three-dimensional (3D) printing technology under a large-deformation regime. The proposed airless tires are designed and fabricated based on the hexagonal lattice geometries under two different orientations. Experimental tests are conducted to investigate the effects of geometrical parameters and the types of lattices on the radial responses of airless tires. A finite-strain beam element is also established to simulate airless tires under various loading states, including radial, longitudinal, torsional, slipping, and rolling conditions. In this respect, a finite-element formulation is developed based on finite-strain hyperelasticity and solved by implementing an iterative Newton–Raphson scheme. Numerical and experimental results confirm that the proposed finite-strain beam element can be used for the analysis of airless tires with complicated lattice geometries under various nonlinearities, such as geometrical, material, and contact phenomenon. The numerical illustrations emphasize the effects of geometrical parameters of lattices and loading parameters on the behavior and mechanical properties of airless tires. The effects of lattice orientations, thickness, number of unit cells, and the coefficient of Coulomb friction between the tire and the ground, as well as loading direction, are investigated. Their implications on the responses of the airless tires with the same weight are highlighted, and pertinent conclusions are outlined. It is also shown that the proposed mathematical model can be used in future efforts for analysis, optimization, and design of lattice-based airless tires with complex geometries.

Practical Applications

This paper is a numerical/experimental research of the 3D printed lattice-based airless tires under various real loading cases such as radial, longitudinal, torsional, slipping, and rolling conditions. The proposed airless tires are designed/fabricated based on two different orientations of hexagonal lattice geometries. The material used for modeling and fabrication of these airless tires is rubber-like materials (hyperelastic), which can have many reversible deformations. The results show that under real loading conditions, the links of the lattice experience instabilities, such as buckling and snap. It should be mentioned that these instabilities are quite important in practical applications that are investigated in the present work in detail. Moreover, the behavior of lattice-based airless tires under each loading condition is divided into linear behavior and nonlinear behavior. Linear behavior of an airless tire can be predicted by the present model for different geometrical parameters (such as length, thickness, among others). Unlike linear behavior, nonlinear behavior highly depends on load and deformation histories. Therefore, each case needs the optimization and design of lattice-based airless tires.

Abstract

Many engineering materials have coupled nonlinear viscoelasticity and viscoplasticity, which are affected by complex thermomechanical loadings. This study addressed the challenge of accurately separating the viscoplasticity and the nonlinear viscoelasticity and formulated the viscoplasticity by considering the effects of temperatures and loading levels. First, the nonlinear viscoelastic constitutive equation was adopted to accurately separate the viscoplasticity and the nonlinear viscoelasticity. Then a kinetics-based viscoplastic model and a new viscoplastic activation energy indicator are proposed to consider the effects of the temperature and loading level on the viscoplasticity. As typical nonlinear viscoelastic viscoplastic materials commonly used in pavement engineering, asphalt binders were selected to demonstrate the principles in this study. It was found that the proportion of the viscoplastic strain is larger than the nonlinear viscoelastic strain for virgin asphalt binders (VBs) and it increases with the temperature, whereas the opposite is true for high-viscosity modified asphalt binders (HVBs) and rubber asphalt binders (RBs). The logarithm of the viscoplastic strain rate increases linearly with the reciprocal of the temperature, and the viscoplastic strain rates at different temperatures are correlated and can be predicted based on the established viscoplastic strain kinetics model. The viscoplastic activation energy indicator can characterize the viscoplastic deformation resistance for nonlinear viscoelastic viscoplastic materials, and the order of the viscoplastic deformation resistances of the three binders was $\mathrm{VB}<\mathrm{HVB}<\mathrm{RB}$, based on this indicator.

Practical Applications

This work presents a theoretical framework that clarifies the deformation characteristics of engineering materials. We separated the viscoplasticity and nonlinear viscoelasticity, and formulated a nonlinear viscoelastoplastic kinetics model for engineering materials by considering the effects of temperatures and loading levels. The developed model can reveal the deformation characteristics of asphalt binders at different temperatures and loading levels according to laboratory test results. Some calculated mechanical indicators of asphalt binders are inaccurate; we addressed this problem using the proposed model. Specifically, we employed the separated viscoplastic strain to improve the calculation accuracy of the nonrecoverable creep compliance and percentage recovery of asphalt binders. We adopted the proposed viscoplastic activation energy indicator to evaluate the viscoplastic deformation resistance of asphalt binders. Overall, we expect practitioners to use the framework to calculate relevant mechanical indicators more accurately and better evaluate the resistance to permanent deformation of engineering materials.

The Darcy–Brinkman flow through a tapered channel or cone, including the flow through a slit or hole on a plate, is studied for the first time. Assuming small Darcy numbers, the solution is found to third order error using the method of matched asymptotic expansions. There are complex interactions between the outer flow and the boundary layer. Streamlines, velocity, pressure, and shear stress are determined. The results are important for the determination of forces and the modeling of transport phenomena.

In view that cities will continue to house the majority of the world’s population at an increasing rate in the face of climate change, this paper studies urban resilience by examining the response history of the mean-square displacement of the citizens of large cities prior to and upon historic natural hazards strike. The recorded mean-square displacements of large numbers of cellphone users from the cities of Houston, Miami, and Jacksonville when struck by hurricanes Harvey 2017, Irma 2017, and Dorian 2019 together with the recorded mean-square displacements of the citizens of Dallas and Houston when experiencing the 2021 North American winter storm suggest that large cities of average population density when struck by natural hazards are inherently resilient. The recorded mean-square displacements presented in this study also validate a mechanical model for cities, previously developed by the authors, that is rooted in Langevin dynamics and predicts that following a natural hazard, large cities revert immediately to their initial steady-state behavior and resume their normal, preevent activities. The inherent ability of large American cities to revert to their normal, preevent, steady-state response as evidenced in this study by the recorded mean-square displacement of their citizens needs to be further explored for other cities around the world with different resources, and socioeconomic structures.

Abstract

Sound transmission loss (STL) can be augmented in buildings using graphene nanoplatelets (GPLs) and metamaterials. The present study established an analytical model grounded on the three-dimensional (3D) elasticity theory to predict STL in a doubly curved shell with a 3D re-entrant auxetic cellular core (3D-RACS) and GPLs as the top layer. The state space method was used to offer an analytical solution, where each part of the structure was divided into a number of layers and each layer into several sublayers. The stiffness matrix of the core was developed according to elastic properties such as Young’s modulus, shear modulus, and Poisson’s ratio out of the plane. The findings revealed that GPLs as the top layer had a tremendous impact on the structure’s performance. Furthermore, the effects of 3D-RACS and GPL parameters on the structure’s STL were investigated in the stiffness and mass control domains. Accordingly, the addition of the core material significantly affected high frequencies, particularly in the mass control domain. Finally, the results indicated that curvature and coincidence frequencies could be changed by optimizing 3D-RACS and GPL parameters.

Practical Applications

Doubly curved structures have different applications in different industries, and due to the complexity of their modelling, they have been used less in research. Nowadays, structural vulnerability to acoustic waves is a concern in the industry, and designers seek to prevent the transmission of acoustic waves into the structure. This is why the study of sound transmission loss is so broad. One of the best methods is to increase the rigidity of the structure because increasing the stiffness of the structure increases the sound transmission loss. In this regard, auxetic materials (3D-RACS) used as a type of metamaterial can have a significant impact on increasing the loss of sound transmission. Due to the use of a sandwich structure in this research, however, GPL material is used for the outer wall exposed to waves. This material can increase the structural rigidity of a structure despite its lightness. Finally, by designing such a structure and comparing the results, a very effective output has been obtained.

The impulse–response (IR) test is the most commonly used field procedure for assessing the structural integrity of piles embedded in soil. The IR test uses the response of the pile to waves induced by an impulse load applied at the pile head in order to assess the condition of the pile. However, due to the contact between the pile and the soil, the recorded response at the pile head carries information not only about the pile, but about the soil as well, thus creating the as-yet-unexplored opportunity to characterize the properties of the surrounding soil. In effect, such dual use of the IR test data renders piles into probes for characterizing the near-surface soil deposits and/or soil erosion along the pile–soil interface. In this article, we discuss a systematic full-waveform-based inversion methodology that allows imaging of the soil surrounding a pile using conventional IR test data. We adopt a heterogeneous Winkler model to account for the effect of the soil on the pile’s response, and the pile’s end is assumed to be elastically supported, thus also accounting for the underlying soil. We appeal to a partial differential equation (PDE)-constrained-optimization approach, where we seek to minimize the misfit between the recorded time-domain response at the pile head (the IR data), and the response due to trial distributions of the spatially varying soil stiffness, subject to the coupled pile–soil wave propagation physics. We report numerical experiments involving layered soil profiles for piles founded on either soft or stiff soil, where the inversion methodology successfully characterizes the soil.

Structural system identification is critical in resilience assessments and structural health monitoring, especially following natural hazards. Among the nonlinear structural behaviors, structural damping is a complex behavior that can be modeled as a multiphysics system wherein the structure interacts with an external thermal bath and undergoes thermalization. In this paper, we propose a novel physics-informed neural network approach for nonlinear structural system identification and demonstrate its application in multiphysics cases where the damping term is governed by a separated dynamics equation. The proposed approach, called PIDynNet, improves the estimation of the parameters of nonlinear structural systems by integrating auxiliary physics-based loss terms, one for the structural dynamics and one for the thermal transfer. These physics-based loss terms form the overall loss function in addition to a supervised data-based loss term. To ensure effective learning during the identification process, subsampling and early stopping strategies are developed. The proposed framework also has the generalization capability to predict nonlinear responses for unseen ground excitations. Two numerical experiments of nonlinear systems are conducted to demonstrate the comparative performance of PIDynNet.

Assessing the postdisaster seismic responses of the as-built bridges based on their real-time status is critical to maintaining their seismic capacity and planning retrofits. This task requires a fast and accurate identification and response estimation method, whereas existing methods either adopt model updating requiring detailed design archives or request sophisticated site testing, both of which are time-consuming and labor-intensive. In this study, approaches combining system identification methods with response spectrum methods for bridges are investigated. A general state-space representation for bridges considering multisupport excitation is developed for model identification. The assumption of the boundary damping matrix in the multisupport response spectrum (MSRS) method is investigated and proved to eliminate pseudo-damping for general viscous-damping structures. A hybrid frequency fitting method (HFF) and subspace system identification method (SSI) in the time and frequency domains, respectively, are examined, and approaches to extracting equivalent boundary stiffness and damping from the identified structural models are studied. The MSRS method is adapted to both identification methods. Numerical simulations and experiments are used to validate the identification approaches in the estimation of boundary conditions. The models identified from the shake table experiments are further used in evaluating its seismic responses. The results of the MSRS method are compared with those from the spectral analysis method showing that the HFF method performs well both in identifying the bridge model and estimating the structural responses. Whereas, the SSI-based methods fail to give a good estimation of boundary damping, and thus cannot directly apply to the MSRS method.

Turbulent flow characteristics around four-pier arrangements are experimentally investigated using particle image velocimetry (PIV). Four wall-mounted piers were arranged in a square configuration at 0° and 90° orientations with different gap-to-pier diameter ($G/D$) ratios. The study shows an intense horseshow vortex system in front of the pier group at 90°. The kinetic energy increased almost six times with $G/D$ ratio for a square configuration at 90° orientation for a given flow condition. Vortex shedding frequency was studied using spectral analysis and Strouhal number corresponding to dominant frequencies for all cylindrical configurations. High energy vortices were observed in between the piers indicating high turbulence in the region. The square configurations with $G/D=2$ at 0° and $G/D=3$ at 90° were found to produce intense turbulence in the flow field as compared to other configurations for the given flow condition. The kinetic energy budget showed that the production rate was significantly higher than the dissipation rate. The square configuration with $G/D=1$ causes minimal perturbations along the centerline when placed at a 90° orientation.

This paper presents a semianalytical methodology for the nonlinear vibration of a functionally graded microplate under transverse patch loadings. The higher-order shear deformation theory (HSDT) is combined with the modified strain gradient theory (MSGT) to model the microplate. The power-law function is used to model the functionally graded material. Hamilton’s principle is used to obtain the governing partial differential equations of motion, which are then solved using Galerkin’s method. The nonlinear free and forced vibration responses are obtained using the incremental harmonic balance (IHB) method, where the incremental part is performed using the arc-length continuation methods. The dependence of the steady-state amplitude on the amplitude of initial perturbation is studied using time history plots. These are plotted using the Newmark-$\beta$ method. The effects of various parameters such as the power-law index, thickness of plate, thickness to material length scale parameter ratio, damping coefficient, different boundary conditions, and different positions of patch loading and its concentrations on the nonlinear free and forced vibration characteristics are examined in detail.

The vehicle–bridge coupled (VBC) vibration problem under the excitation of road roughness is essentially a nonstationary random vibration problem. At present, the computational efficiency is still the key factor of restricting the application of the stochastic vibration theory in nonlinear dynamic systems. In this study, the covariance between the system excitation and response is used to recursively solve the variance of the system response, and an efficient numerical method of solving the evolutionary statistical moments of dynamic responses of the time-variant VBC system is proposed. The study shows that the results obtained by the recursion method are consistent with the explicit time-domain method, and are further verified by the Monte Carlo method. Furthermore, the method proposed is applied to study the impact factor spectrum of highway beam bridges. The deficiency of the existing impact factor spectrum formula is pointed out, and an effective method is put forward.

The ballast, essentially unbound granular material, contributes more than 50% to the total settlement of the ballasted railway track, greatly affecting the safety and comfort of train operation. To reduce the deformation-related distress in the trackbed, predicting the development of irreversible deformation in the granular material is a crucial issue. Therefore, to better calculate plastic deformation in the ballasted trackbed, this study extends the existing cyclic densification model to a more realistic loading condition by incorporating the impact of principal stress rotation (PSR). We first investigated the evolution characteristics of PSR-induced irreversible deformation in the granular material via discrete element method (DEM) simulations, on the basis of which appropriate reduction of the shakedown threshold and modification of the contraction/dilation function for the frictional sliding mechanism were then introduced to realize the consideration of the effect of PSR in the original cyclic densification model. Subsequently, after determining the modification coefficients through model calibration taking the DEM result as the benchmark, the proposed model was employed in a full-scale physical model and on-site track test, respectively, to predict long-term accumulative settlement in the ballasted trackbed subjected to actual train loading. Results indicated that the proper reduction or modification of relevant parameters reflected the effects of PSR on accumulating permanent deformations at the granular trackbed well. Furthermore, the modified cyclic densification model gave more reasonable predictions of plastic strain in the granular trackbed under actual train loading than the original model. Overall, our findings apply to the prediction of long-term postconstruction accumulative settlements in practical engineering, having broad application prospects.

A new gradient-enhanced damage model is developed based on a new equivalent strain. This new equivalent strain is derived using the Menétrey–Willam yield function. The proposed model is implemented in a three-dimensional framework via 10-node tetrahedral element. Excessive spread of damage observed in the gradient-enhanced model is prevented by adopting a novel variable and anistropic nonlocal length scale. Performance of the model is investigated by comparing a wide variety of benchmark examples used in the literature. Obtained results show that proposed model is able to characterize the complex stress states, such as mixed-mode fracturing and nonplanar cracking as well as tensile-dominated fracturing.