Journal of Engineering Mechanics

Studying ultrasonic guided wave modes in multiple steel wires helps extend and apply wave dynamics theory to practical engineering. This research focused on elastic wave propagation for investigating dispersion behavior in a helical waveguide under the prestressed state. For the guided wave theory of one-dimensional propagation, the physical system represented as a curve must satisfy translation invariance. Elastic wave propagation in a helical waveguide was analyzed using the semianalytical finite element (SAFE) method. The scaled Frenet–Serret and twisted basis dispersion curves were analyzed for comparison. The bases were used to define covariant and contravariant bases where the strain and stress tensors were expressed. Then, by proving the translational invariance of the system in the curvilinear coordinates, a Fourier transform of the displacement was deployed to distinguish plane waves based on their wavenumber and reduce the study of the waveguide according to its cross-section. Later, the SAFE method derived from the twisted cylindrical coordinate system was compared with the standard axisymmetric SAFE method. Analysis of an outer steel wire of the seven-wire helical strand was carried out for undamped and damped cases with initial prestress conditions to investigate the dispersion behavior of the helical waveguide. Static analysis of the entire seven-wire helical strand was carried out by considering an initial prestress field, and a finite-element method based on asymptotic expansion theory was used to solve contact stress field calculation. Correspondingly, the proposed method was verified with the classical Machida and Costello calculation theories for calculating the stress field on its respective axial cross-section for each wire. A very complex band diagram needs to be investigated while performing a dynamic analysis of the helical waveguide. The current work introduces the modal filters via the so-called coupling conditions to parse the complex dispersion characteristics. When the SAFE method is used to analyze its dynamic wave properties, the employed coupling condition reduces the degrees of freedom of the system and improves calculation efficiency. Henceforth, the proposed methodology for calculating the prestressed state is the potential health monitoring scheme for a helical multiwire.

Abstract

To ensure the safety of concrete structures under fatigue loading, the fatigue crack propagation in concrete needs to be evaluated accurately. In this paper, a numerical method for mixed mode I-II fatigue crack propagation in concrete is proposed, in which the stress intensity factor (SIF)-based crack propagation criterion is employed, and the degradation of the cohesive force under fatigue loading is considered quantitatively. To validate the applicability of the numerical method, the mixed mode I-II fatigue fracture test of the three-point bending (TPB) beam is conducted. The fatigue crack propagation length is measured with the digital image correlation (DIC) method. Eventually, the applicability of the numerical method is validated by a reasonable agreement between the numerically derived crack propagation path, crack mouth opening displacement (CMOD), crack mouth sliding displacement (CMSD), crack propagation length, and mode I SIF and the experimental results. It is concluded that the proposed numerical method can be used to evaluate the mixed mode I-II fatigue crack propagation process of concrete when the initial fracture toughness, Poisson’s ratio, and Young’s modulus under static loading and the tension-softening constitutive relation under fatigue loading are given. In addition, the experimental results indicate that the mixed mode I-II fatigue failure of concrete occurs when the mode I SIF reaches a critical value, regardless of the fatigue load level and the fatigue life. The numerical results show that the mixed mode I-II fatigue crack propagation path is independent of the fatigue load level and approximately identical to that under static loading.

Practical Applications

In practical engineering, many concrete structures such as concrete pavements may be subjected to fatigue loads, e.g., cyclic vehicle loads. Under the fatigue loads, the crack would initiate, propagate, and even cause the fatigue failure of the concrete structures. Meanwhile, due to the complexity of the fatigue loads, the crack path could not be predicted in advance, making the evaluation of the fatigue performance more difficult. Therefore, a thorough investigation of the fatigue fracture properties of concrete is of great theoretical significance and practical application value. In this study, a numerical method for predicting the mixed mode I-II fatigue fracture performance of concrete is presented. With the numerical method, the crack propagation length, crack propagation path, deflection, crack opening displacement, crack sliding displacement, and eventual fatigue life of the concrete structures could be reasonably predicted. The numerical results could provide significant references to the fatigue life prediction of concrete structures in service, such as concrete pavement. In addition, the predicted fatigue crack length and crack path would also be helpful to the reinforcement and repair of concrete structures.

This paper establishes a comprehensive modeling for permeability of porous solids incorporating cracks with clustering extent ranging from nonoverlapping to percolation. The geometry of cracks is characterized through the crack density, orientation, connectivity, and fractal dimension of crack networks. The interaction direct derivative (IDD) model from effective medium theory is developed to predict the permeability of solids with nonoverlapping cracks and further extended by a two-step scheme to account for cracks with local clustering. The continuum percolation theory is adopted to build the permeability scaling law for crack networks approaching percolation. The comprehensive model thus established was validated against numerical simulations for crack networks with different geometry characteristics. The obtained results show that (1) the classical IDD model can predict satisfactorily the permeability for nonoverlapping cracks and the crack opening has nearly no impact on overall permeability, (2) the extended IDD model considers successfully the local clustering of cracks, the prediction range is greatly enhanced for overall permeability, and the impact of crack opening is still limited, and (3) as crack networks approachi percolation, the overall permeability observes a scaling law highlighting the importance of crack connectivity, and the impact of crack opening assumes a power law with the exponent related to the fractal dimension of crack networks.

Particle morphology is a basic inherent feature of granular materials that plays an important role on their macroscopic behaviors. A multiscale description of particle morphology is generally developed from three levels: large (general form), medium (local roundness), and small (surface roughness). The morphological features of two typical natural sands (Fujian sand and calcareous sand) were investigated in the present study based on spherical harmonic (SH) analysis. Three-dimensional (3D) printing was employed to develop the mass manufacture of grains with independent control of morphology and material properties. Full-scale morphologies of the sphere, Fujian sand (FS) as well as calcareous sand (CS), and single-scale morphologies of calcareous sand at large-(CS24), medium-(CS58), and small-(CS915) levels were printed. A series of triaxial tests were performed on these printed grains to explore their strength-dilation behaviors. The results suggested obvious strain-softening and volume-dilation behaviors were observed at a confining pressure varying from 20 to 100 kPa. A significant enhancement of both shear strength and bulk dilation was indicated from irregularly shaped particles compared with the volume-equivalent spheres. Also, the morphologically derived enhancement of shear strength is weakened from the general form to surface roughness while the enhancement of dilation is the strongest at the medium-scale level of local roundness, indicating different morphological origins between strength and dilatancy. In addition, Bolton’s dilatancy coefficient is a fixed value of 0.452 in this paper, independent of particle shape.

This paper investigates the influence of time-dependent bond slip on the delayed failure of RC frames. The time-dependent model of bond slip is formulated based on the mechanism of subcritical damage accumulation along the steel–concrete interface. A kinetic model of the time dependence of slip under sustained loading is developed through numerical simulations. The model is incorporated into a recently developed reduced-order numerical model for simulations of the progressive collapse of RC frames. It is shown that the present model captures the essential deformation mechanisms of the frame under both monotonic loading and sustained loading, and that the time dependence of bond slip has a profound influence on the delayed failure of RC frames, especially under moderate sustained loading. This finding highlights the importance of understanding and accounting for the time dependence of bond slip for future study of the delayed progressive collapse of RC structures.

Fastening systems play a significant role in railroad track dynamics. In this paper, three approaches are investigated for rail fastenings modeling using FEM: (1) spring–damper pairs covering the areas representing the fastening connections; (2) a solid-load approach that explicitly models the solid baseplates and includes toe loads by applying external loads; and (3) a solid-spring approach that takes into account the coupling of rail with the ties by using prestressed springs. Experimental tests were carried out to evaluate the performance of the FEM models. The mode shapes obtained from the FEM models and the experiments were used for the evaluation. A measurement quantifying the similarity of the mode shapes was proposed, which considers both shape similarity and distance similarity. The results showed that the rail foot’s mode shapes obtained from the model using the spring–damper approach demonstrated the most similarity with the ones obtained from the experiments.

Accurate estimation of blast loads on a structure requires consideration of several complex phenomena during interaction with the target surface. One such phenomenon is the clearing effect observed during the diffraction of blast waves from finite reflecting targets. A clearing wave is generated due to the pressure difference between the edge and internal locations of the target surface, which reduces the reflected impulse at the considered location on the target surface. The state of the practice relies on simplified empirical methods to predict the clearing effects, which are often inaccurate or may also be unconservative. Past analytical studies on the clearing effect have mainly focused on weak blast, where the clearing wave speed is assumed to be the ambient sound speed. In the present study, the authors propose a methodology to include the effect of clearing on reflected overpressure history for strong blasts by considering an average clearing wave speed computed using the ideal gas law. The modified approach was verified and validated with existing literature and benchmarked against numerical studies. The proposed clearing methodology was shown to address the limitations of the current state of practice. Finally, a simplified version of the proposed clearing model was presented in the form of charts that can be used to compute the reflected overpressure history, including the effect of clearing on a finite-surface rectangular target.

This work investigated the effective structural and functional behavior of shape-memory alloy (SMA)-based triply periodic minimal surface foams based on the Schwarz primitive (P-foams) using finite-element analysis (FEA) and numerical homogenization methods. The effect of relative density and applied temperature on the homogenized mechanical behavior of the SMA foam, including its superelasticity, and the evolution of the effective martensite volume fraction with the applied load was investigated considering axial and shear loading cases. In contrast to dense SMA, the effective martensite volume fraction in the considered foam was found to vary exponentially with the strain in the case of monotonic loading, asymptotically approaching 1 as the strain increased indefinitely. Moreover, the effective superelasticity of the SMA P-foam was found to be facilitated by decreased temperature and relative density. The onset of phase transformation for the P-foam under various loading scenarios was shown to be well approximated using an extended Hill loading surface.

On-board monitoring of track irregularities and bridge dynamic characteristics based on vehicle vibration responses provides basic data for the condition assessment of high speed railway bridges. However, the identification process inevitably introduces estimation uncertainty because of measurement noise and system parameter uncertainty. Here, in a probability framework, we propose a recursive Bayesian Kalman filtering (RBKF) algorithm for quantifying the identification uncertainty of the track irregularities and bridge natural frequencies. A nonlinear state-space model with measurement noise and process noise was first established for vehicle-bridge (VB) systems. Then the RBKF algorithm was formulated using a nonlinear state-space model, and the identification uncertainty was quantified in terms of estimation variances. A numerical study of two high speed railway bridges validated the RBKF algorithm. This study may help develop new approaches for on-board monitoring and condition assessment of high speed railway bridges.

Formulation of governing equations for an elastic cable have a long and dated history. A unified framework to detect the dynamics of such systems is detailed, justified, and assessed numerically. Modal analyses are performed in the Frenet basis, which describes the motion in the local frame and accounts accurately for the system’s physics. In this article, a methodology to produce arbitrary reduced-order models for cable nonlinear dynamics is provided. The results obtained from the latter via direct time integration are challenged numerically via a comparison with results of the nonlinear finite-element method.

This paper investigates several granular interaction laws used in the modeling of discrete granular media. In the considered model, each grain interacts with its neighbors with a coupled shear-normal interaction law. The analysis is performed in a geometrically exact framework allowing large rotation and displacement evolutions, without any geometrical approximations. It is shown that most of the granular interaction laws available in the literature are classified as hypoelastic interaction laws, and we precise the requirements to build some hyperelastic interaction laws that avoid artificial dissipation. We also show that the uncoupled granular interaction law is hyperelastic for all the studied models. The analysis is applied to a paradigmatic elementary system of a granular loop with a diamond pattern (a four-grain cyclic granular chain) loaded by concentrated forces. Instabilities are observed for large displacement of the diamond chain for all the classified models. It is observed that the discrepancies between each model may grow during the deformation process. The instability phenomenon is associated with the appearance of a limit load for this granular structural problem due to large nonlinear geometrical effects. Blocking phenomena may also appear for such granular structural systems due to secondary granular contacts.

Engineering structures in the field are exposed to three-dimensional (3D) stress-displacement conditions with fabric evolution occurring within the soil–structure interface. Upon 3D shearing, the fabric of the interface would change with shear displacement, which influences the dilatancy or plastic flow response of the interface. To consider the 3D stress state and fabric effect, an enhanced fractional model for the interface under monotonic and cyclic loads is developed by using a multiaxial loading vector, a fabric-dependent plastic flow vector, and a kinematic hardening rule. The developed model has three key features: (1) 3D stress-displacement response with shear coupling in different directions is considered by the 3D elastoplastic relation; (2) fabric-dependent dilatancy state line of the interface is captured via a fabric scalar; and (3) dependence of particle breakage on the critical state line of the interface is also considered by introducing a shift stress. To validate the proposed model, a series of test results obtained from the interface direct shear test and simple shear test are simulated. Discussions on model performances with and without considering the fabric effect are then carried out. It is found that the developed model can capture the key features, e.g., hardening/softening, dilatancy/contraction, and strength degradation, of different soil–structure interfaces. The evolution of the fabric scalar mobilized the dilatancy state of the interface under cyclic loads, through which the remarkable normal contraction response under cyclic loading is successfully captured when compared to those without considering fabric effect.

Abstract

The radial layout D2Q9 lattice Boltzmann model applied to elastic lamina was investigated. An equivalent differential discursive form for the equation of elastic lamina deformation is provided, and its equivalency to the lattice Boltzmann method (LBM) equation was proved by the Chapman–Enskog expansion. A set of equilibrium distribution functions for the radial layout D2Q9 lattice Boltzmann model and elastic lamina deformation was constructed. The functional form of the external source term is given; thus, the algorithm for the radial layout D2Q9 lattice Boltzmann model was determined. The characteristics of deformations of elastic lamina with different load patterns (loaded evenly on the whole area, loaded linearly on the whole area, loaded evenly on the left half area, and concentrated in the center) were simulated using this model. Numerical tests were conducted to compare the numerical results and the analytical solutions. This work demonstrated that the radial layout D2Q9 lattice Boltzmann model can be used to solve elastic lamina deformations. This paper provides a novel numerical method for computing the deformation of elastic lamina, and has the potential for further application in fluid–structure interaction.

Practical Applications

A lattice Boltzmann model that can calculate the deformation of elastic thin plates is proposed in this paper. The model adopts the general format of fluid simulations on the lattice format, and this paper shows it to be applicable for solving problems involving elastic systems. The model can be applied to both fluid and solid simulations if appropriate equilibrium distribution functions are selected. Because the general format is adopted in this model, the model has advantages in dealing with the fluid–structure interaction boundary problem, and has the potential to simplify LBM programs involving fluid–structure interaction problems and improve the computation efficiency of the LBM. The model can be applied to fluid–structure interaction computation in fields of civil structures, machinery, biomechanics, and so forth, such as for the displacement of high-rise buildings under a wind field, the response of wind turbines under excitation, the interaction of blood and vessels, and so on.

In the framework of generalized plasticity theory, this paper presents a new elastoplastic model to characterize complicated softening/hardening and dilation/contraction behaviors of sand–gravel composites in triaxial tests. The model has six parameters that are determined by the conventional triaxial test directly, which is of great practical interest to engineers. The dilatancy equation that is able to describe the dilatancy of sand–gravel composites during the whole shearing process is incorporated into the model. The advantage of the proposed model in predicting the dilatancy behavior of sand–gravel composites is demonstrated by comparing it with three widely used dilatancy equations. A set of drained triaxial compression tests were launched to examine the performance of the proposed model. In addition, the applicability of the model is also confirmed by sand–gravel composites tests covering a wider range of confining pressure in previous literature. The generality of the model on other granular materials including rockfill, Ottawa sand, calcareous sand, cement-sand–gravel material, and glass beads mixtures is also verified by comparing the experimental results with the corresponding fitting results. Furthermore, the proposed model is programmed into the nonlinear finite element program GEODYNA and applied to the numerical simulation of high concrete-faced sand–gravel dams. Summarizing the fitting and numerical results comprehensively, the constitutive model proposed in this study is capable of characterizing the mechanical behaviors of granular materials and can provide a powerful tool for geotechnical engineering.