Journal of Engineering Mechanics

Intelligent compaction (IC) of asphalt pavements is an emerging area of research that attempts to extend mechanistic-empirical design principles to the construction of asphalt pavements. These techniques monitor the vibrations of the compactor and vary the roller parameters in real time to ensure adequate and uniform compaction. Although these techniques are in various stages of field demonstration, their performance is still being verified. The lack of established theoretical foundations has limited the widespread acceptance of these techniques. In this paper, a viscoelastic-plastic (VEP) model is used to simulate the behavior of vibratory rollers during the compaction of asphalt pavements. The VEP model is shown to be relatively accurate, computationally tractable, and in a form that is conducive to numerical simulation. Comparison of the simulation results with data gathered during construction of asphalt pavements indicate that this model can serve as the basic theoretical foundation for the realization of intelligent compaction of asphalt pavements.

The optimum design of an additional intermediate support is investigated for raising the fundamental natural frequency of a beam or column subjected to compressive axial loadings. First, the criterion that constitutes the general characteristic equation of the optimal attachment position is explicitly provided so that an objective value of the fundamental frequency can be achieved with the minimum restraint stiffness of the intermediate support. Then, the optimum design of an intermediate support is performed for three illustrative beams of different classical boundary conditions to demonstrate the effects of the compressive axial loads. Numerical results show that the axial load can remarkably influence the support design of its optimum position and minimum stiffness when using it to increase the beam fundamental frequency.

Studies of the bearing capacity of footings usually do not take into account the effect of the intermediate principal stress. In practice, the intermediate principal stress has certain influences on the strength of geomaterials (e.g., rock and soil) or concrete. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua (FLAC) and the united strength theory (UST) to investigate the influence of the intermediate principal stress on the bearing capacity of strip and circular footings. A series of numerical solutions are presented to determine the vertical bearing capacity of strip and circular footings using an elastic–perfectly plastic constitutive model following UST and the associative flow rule. First, the bearing capacity of flexible and strip footings according to UST and other criteria are compared. Second, three bearing capacity factors ($N_c$, $N_q$, and $N_{\gamma }$) are evaluated for strip and circular footings subjected to centered vertical loads with rough interfaces. A certain influence of the intermediate principal stress on the bearing capacity of strip and circular footings was detected based on UST and the associative flow rule. It was found that the intermediate principal stress has more influence on the bearing capacity of a strip footing than the bearing capacity of a circular footing. It was also found that the bearing capacity factor $N_{\gamma }$ is more significantly influenced by the intermediate principal stress than are the factors $N_c$ and $N_q$. The influence of the intermediate principal stress on three bearing capacity factors for strip and circular footings analyzed in this paper has been obtained using the elastic–perfectly plastic constitutive model based on UST.

Dynamic response of mechanical structures is significantly affected by joints. Joints introduce remarkable frictional damping and localized flexibility to the structure; hence, to obtain a more accurate representation of a system's dynamics, it is crucial to take these effects into account. This paper investigates the application of finite-element model updating on characterization of a nonlinear joint interface. A thin layer of virtual elements is used at a joint location to represent the nonlinear behavior of the coupling in the tangential direction. The material properties of the elements are described by a nonlinear constitutive stress-strain equation that defines the nonlinear state of the joint interface. In this study, Richard–Abbot elastic-plastic material was considered, which is capable of characterizing energy dissipation and softening phenomena in a joint at a nonlinear state. Uncertain material parameters are adjusted to minimize the residual between the numerical and experimental nonlinear frequency responses. Minimization was carried out based on iterative sensitivity-based optimization. The procedure was implemented on an assembled structure consisting of two steel threaded pipes coupled to each other by a nut interface. It was demonstrated that the proposed technique significantly reduced the uncertainties in the joint modeling and led to a more reliable description of the assembled structure.

This paper presents a mathematically exact solution of the continuum to the transient response of a vertical single beam buried partly in a nonlinear foundation because of a support displacement. The foundation has a nonlinear property between reaction and displacement similar to elastoplastic foundation and viscous damping of the Voigt type. Winkler’s hypothesis can be produced from the relative displacement based on a foundation displacement, which may be imitated by behavior of a one-dimensional shear wave in the medium. The approach, which involves the classical beam theory and the method of eigenfunction expansion, is simple and clear for seeking solutions and solving equations of motion under the boundary and initial conditions. The connection conditions on the mechanics at the interface and the continuity for displacement and its velocity at the changing time are effectively applied to the relationship between the governing equations of motion satisfied in an elastic domain and those satisfied in a plastic domain.

The installation of a drop pool in an open channel is aimed to dissipate the flow energy that diminishes the destruction of the downstream channel. Previous studies have been conducted experimentally on the hydraulic properties for flow over the pools. The numerical simulations based on the Reynolds average Navier-Stokes (RANS) equation and the renormalization group method (RNG) $k\text{-}\epsilon$ turbulent transport model for exploring the dynamic characteristics of the skimming flow over the vertical drop pools are presented. The simulations were conducted for a specified supercritical approaching flow on a fixed drop height $H$ but different heights of the end sill $h$. The simulated results were verified by previous experimental results of the flow visualization and the measured mean velocity profiles. The numerical results show that the skimming flow will form in cases of $h/H\geqq 4/14$ where the dropping flow slides over the pool and forms a sliding jet. The pressure tends to be negative at the leading edge of the wall corner in the vertical drop area for a low-end sill. The momentum exchange between the sliding jet and pool creates a circulation flow in the pool; the major turbulent energy dissipation occurs at the momentum exchange zone. The maximum vorticity occurs at the drop corner where the sliding jet starts. The head loss of energy decreases as $h/H$ increases. The empirical formula of the energy loss between the approaching flows and downstream flows is presented.

The linear response of a flexible longitudinal pole hitting a column or beam is investigated. Based on Timoshenko beam theory, an efficient analytical solution method using mode superposition for the coupled beam-pole system is presented. Any physical set of boundary conditions can be accommodated, such as a free pole impacting a column with arbitrary boundary conditions or a free-free beam hitting a pole that is either pinned or free at the opposite end. For the case of the free-free beam, it can have arbitrary initial translational and rotational velocities. Impact can occur anywhere within the beam span, although the contact is frictionless. It is shown that, when the beam response governs, the initial impact is likely governed by shear, and therefore, Euler-Bernoulli beam theory is not a good modeling choice in general. Results based on a wood log hitting concrete, steel, and wood columns reveal the behavior governing the impact force time history. A simple design formula for the initial maximum impact force is shown to be quite accurate. The impact duration is governed by either the longitudinal wave speed in the pole or the shear wave speed in the column. In addition, the energy transfer between translational and rotational kinetic energies and strain energies is used to analyze the impact vibrational motion; this analysis reveals both the initial dependence on shear deformation and the transfer of the associated energy to bending energy. The significance of including rotary inertia is also demonstrated.

The heterogeneous internal structure of quasi-brittle materials governs several aspects of their behavior, especially in the nonlinear range. Size and spacing of weak spots (e.g., aggregate-matrix interfaces, flaws, and slip planes) where failure is likely to occur are two of the most important material characteristic lengths that can be used to characterize the micro- and meso-structure of these materials. Discrete (lattice and particle) models can be conveniently used to directly model these geometrical features, but they tend to be computationally expensive, and consequently, the derivation of macroscopic continuum-based approximations is often highly beneficial. The current study demonstrates that the continuum macroscale approximation of discrete fine-scale models leads naturally to a high-order microplane theory characterized by multiple characteristic lengths. The average weak spot spacing is shown to be associated with strain gradient effects; whereas the average weak spot size is shown to be associated with the Cosserat characteristics of the theory. The formulated microplane theory is compared with and contrasted to classical continuum theories available in the literature. Finally, for strain softening, known in the case of first-order local formulations to cause strain localization in an unrealistic vanishing size volume, a localization limiter capable of enforcing the minimum localization size to be of a finite value is formulated, exploiting the spectral wave propagation analysis approach.

A three-dimensional exact free vibration solution for plates made of functionally graded materials is provided in the current study. An analytical solution in the form of a power series and numerical results for plates having material with an exponential distribution of properties across the thickness are established. Exact solutions for linearly elastic, simply supported, and rectangular plates based on three-dimensional elasticity theory are derived. A power series method is used to find the natural frequencies. An assumed displacement field identically satisfies all the boundary conditions. Numerical results for frequencies are provided for exponentially graded thick and thin plates. The presented results should serve as benchmark frequencies for exponentially graded plates.

The analytical treatment of normal, rocking, and torsional forced time-harmonic vibrations of a rigid circular disk in a transversely isotropic full-space is revisited. A complete discussion on frequently used contact assumptions of adhesive and smooth models is given, and the effects of different contact models on the results of each vibration mode are discussed. With the aid of appropriate dynamic Green’s functions, the in-plane mode of vibration of the disk is treated analytically for the first time, and the results are expressed in terms of the solution of a Fredholm integral equation. For all four vibration modes, the relations for the contact stress, the resultant force acting on the disk, and the dimensionless compliance factor are given. The available closed-form results in the literature corresponding to the static loading are exactly recovered as the limiting cases of the current study. Furthermore, the results are verified with the special case of an isotropic full-space. By virtue of the contour integration technique as well as the residue theorem, a robust numerical integration technique is proposed to overcome the difficulties in numerical evaluation of the semiinfinite integrals appearing in the obtained Fredholm integral equations of all four modes of vibration. Some plots are provided to present the lateral, vertical, and rocking compliance factors for different transversely isotropic materials. The effects of material anisotropy on the results are also highlighted.

Buckling and vibration characteristics of thin, symmetrically laminated, elliptical composite plates under initial in-plane edge loads and resting on Winkler-type elastic foundation are presented based on the classical laminated-plate theory. The governing equations were obtained from the variational approach and solved by the Ritz method. Extensive numerical data are provided for the first three natural frequencies as a function of in-plane load, and critical buckling loads as a function of aspect ratio for various classical edge conditions (free, clamped, and simply supported). Moreover, the effects of fiber orientation on the natural frequencies and buckling loads of laminated angle-ply plates, with stacking sequence of ${\left[\left(\beta /-\beta /\beta /-\beta \right)\right]}_s$, were studied for chosen foundation parameter. Selected deformation buckling mode shapes are illustrated. The accuracy of calculations was checked by performing good convergence studies, and the correctness of results is established by comparison to existing results in the literature and FEM data.

Analytical solutions have been derived for the onset of strain localization in a broad class of unsaturated elastic-plastic porous materials based on Bishop’s definition of effective stress. Critical hardening moduli for constant water content and drained loadings were found to be further gradual simplifications of the critical hardening modulus for an undrained loading. In addition, the solutions were found to reduce to the previously found solutions for fully saturated and monophasic porous materials by adequately adjusting bulk moduli of the pore fluids. This finding demonstrates that the mechanics of fully saturated and monophasic soils is the special simpler case of the mechanics of unsaturated soils. A diagnostic tool for detection of the inception of strain localization was developed by implementing the aforementioned solutions into a constitutive driver for a bounding surface plasticity model. The tool was used to further illustrate the strain localization behavior of unsaturated Bourke silt from the Bourke region of New South Wales, Australia, subjected to undrained, constant water content and drained loadings.

Cross-property relations are established in this paper between transport and mechanical properties of two-phase composite materials. In particular, the cross-property relations among the effective thermal conductivity (or chemical diffusivity), effective shear, and effective bulk moduli of two-phase composites are developed. Conventional isotropic composite mechanics models are employed to obtain effective properties of composite materials. The effective properties are expressed in terms of volume fraction of the inclusions, and then the volume fraction is used as the link to develop the expressions for the cross-property correlations. The present method can be used together with the recently developed composite damage mechanics method for evaluating cross-property correlations of distressed materials. Because mechanical properties of distressed materials have been investigated extensively, the cross-property relations provide a powerful method for evaluating transport properties of distressed materials without sophisticated experiments. Two numerical examples are shown for the cross-property correlations of distressed concrete under two-dimensional loading, where the isotropic damage is governed. Correct trends were obtained for the two numerical examples.