Journal of Engineering Mechanics

Time-dependent strains in reinforced concrete (RC) members are usually estimated using approximate algebraic methods. This paper presents an exact method for estimating the time-dependent strains in RC members subjected to concentric axial compression, using creep compliance and shrinkage strain information for the corresponding plain concrete. The axial strain in concrete is taken to be the sum of shrinkage strain and the creep strain. Shrinkage strain in concrete is modeled as a: “lack-of-fit” problem. Assuming a linear viscoelastic constitutive law for concrete and a linear elastic constitutive relation for reinforcing steel, the corresponding one-dimensional viscoelastic boundary value problem is solved. It is assumed that there is a perfect bond between concrete and steel. The proposed method is validated using tests reported in the literature. The prediction of overall time-dependent axial strains under applied axial loads is found to match the observed test results closely. However, there are discrepancies in the relative magnitudes of creep and shrinkage strains, and the possible reasons for these are also discussed.

In this paper, the dynamic response of underground rectangular fluid tank resting on an elastic foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The dynamic responses investigated are deflection, bending moment, and shear force of the tank. The underground rectangular tank is assumed to be a frame composed of horizontal and vertical beams resting on an elastic foundation. The mechanical resistance of elastic foundation is modeled using spring elements that account for soil resistance due to compressive strains in the soil. The fluid in the tank is assumed as inviscid and irrotational, and the influence of free-surface wave is ignored. An analytical solution of free vibration modes of empty tank (dry modes) is derived at first, and then the free vibration modes of fluid tank infilled with water (wet modes) can be obtained by the dry modes. Based on the wet modes, the explicit formulations of dynamic responses of the tank are finally obtained by the modal superposition method. The solutions for several cases, such as empty tank and fully filled fluid tank subjected to harmonic loads, are also discussed. Further parametric analysis is carried out to investigate the influence of the soil–structure relative stiffness ratio on dynamic responses of the fully filled fluid tank.

The research reported herein makes use of finite-volume simulations of morphing continuum theory (MCT) to reproduce critical relations of thin-airfoil theory for the simple configuration of a flat plate for supersonic and subsonic flows. With a small mesh size of $N=\mathrm{5,600}$ elements, simulations confirm that inviscid flows simulated by MCT match analytic relations for lift and pressure coefficients derived from classical fluid mechanics, a result confirmed by the inviscid MCT equations. Initial success of MCTHyperFOAM version 1.0 for the flat plate indicates that the solver can be extended to more complex aerodynamic flows.

This paper presents an experimental work aimed at determining the fracture properties of fired-clay and tuff brick, obtained from construction sites of existing buildings and a commercially available fired-clay brick. This paper provides a range of values of the fracture properties of natural and artificial bricks used in existing constructions. Natural and artificial stones are quasi-brittle materials and the cohesive crack model can be used to describe the propagation of cracks in these materials. However, some of the parameters of the cohesive crack model are calibrated against a large set of data of concrete specimens and might not be suitable for other quasi-brittle materials that feature a smaller fracture process zone. In this paper, digital image correlation (DIC) is used to put forward a new approach to measure the critical crack opening $w_c$ and therefore gain a new insight into the fracture parameters of bricks.

Since the middle of the last century, numerous fracture models have been reported in the literature. These models, whether proposed on the basis of theoretical derivation, experimental observation, or a combination of the two, are found to vary greatly from each other in terms of both the forms and complexities in mathematics. Generally speaking, more fracture parameters are supposed to provide a better description of fracture initiation and propagation, which, however, would also create huge obstacles for their application in practice. Instead of proposing a totally new model, it seems more practical to perform a comparative study on the flexibility and operability of existing models for fracture prediction of structural steels. Specifically, the ductile fracture characteristics of Q355 structural steel were first studied experimentally with six types of notched specimens pulled up to failure under monotonic loading. Corresponding numerical simulations were also performed using an enhanced $J_2$ plasticity model. Seven popular fracture models having various numbers of fracture parameters were selected to reconstruct the three-dimensional (3D) fracture loci of Q355 steel and compared in detail. Also, a specially designed flat plate with three holes was tested to failure as an aid to further evaluation of these models at the structural level. The analysis results in this study indicate that, first, the overestimations of the classical $J_2$ plasticity at low stress triaxialities could be corrected by the enhanced one proposed in this study through the introduction of a Lode parameter–related term. Moreover, the enhanced $J_2$ plasticity enables the postnecking hardening relationship and yield criterion to be identified independently, which makes it more convenient in view of the given practical application. Second, the stress triaxiality-only-related fracture models, like the void growth model and Johnson-Cook model, are sufficient for fracture prediction under axisymmetric tension, but in cases of more comprehensive stress states where shear stress cannot be neglected, the fracture resistances would be highly overestimated, leaving a potential threat to human lives. Third, the Wierzbricki-Xue model is more advantageous with a higher fracture prediction accuracy (smaller than 3%) but fewer fracture parameters to be calibrated. Fourth and finally, a flat plate with three holes is a promising specimen in terms of assisting in the evaluation of fracture models because there would be two distinct fracture modes generated simultaneously.

Sand typically exhibits anisotropic internal structure (or fabric), and the fabric anisotropy has a dramatic influence on the mechanical behavior of sand. Meanwhile, the fabric evolves when sand is subjected to external loading. This eventually makes the response of strip footings on sand dependent on fabric anisotropy and fabric evolution. A numerical investigation on this effect is presented using a critical state sand model accounting for fabric evolution. The model parameters are determined based on plane strain and triaxial compression test data, and the model performance is validated by centrifuge tests for strip footings on dry Toyoura sand. The bearing capacity of strip footings is found to be dependent on the bedding plane orientation of dense sand. However, this effect vanishes as the sand density decreases, though the slope of the force-displacement curve is still lower for vertical bedding. Progressive failure is observed for all the simulations. General shear failure mode occurs in dense and medium dense sand, and the punching shear mode is the main failure mechanism for loose sand. In general shear failure, unsymmetrical slip lines develop for sand with an inclined bedding plane due to the noncoaxial sand behavior caused by fabric anisotropy. For strip footing on sand with horizontal bedding, the bearing capacity and failure mechanism are primarily affected by the sand density. The bearing capacity of a strip footing is higher when the sand fabric is more isotropic for the same soil density. An isotropic model can give significant overestimation on the bearing capacity of strip footings.

The stress-strain response of sand at high strain rate is an important topic. However, most of the numerical studies concentrated on sands at high water content and were not able to capture the softening and subsequent stiffening stress-strain behavior observed at low water content. In this study, split Hopkinson pressure bar (SHPB) tests of sands were numerically simulated and the equations of state (EOS) at different water content were calibrated using back calculation. The back-calculated EOSs were used to calibrate a three-phase model capable of capturing the sand response at any water content. The response predicted by the three-phase model was validated by comparing the numerical and experimental stress-strain responses. A parametric study was carried out to understand the effect of interface friction and aspect ratio on the validity of the SHPB results by considering different aspect ratios and interface frictions for the specimens. The results showed that specimens with higher aspect ratio take longer time to achieve stress equilibrium, whereas specimens with interface friction never attain perfect stress equilibrium.

A constitutive model is presented for the hysteretic behavior of elastomeric material, called the modified generalized Maxwell model (MGMM). A new force-displacement relationship that describes the well known generalized Maxwell model (GMM) is also proposed in this study and forms the basis for the MGMM. This relationship can be used regardless of the number of Maxwell elements. The damper was first characterized using terms of the viscoelastic (VE) material, determining its shear storage modulus and loss factor for a range of cyclic tests. This led not only to an understanding of how the main mechanical properties of the damper change when the strain amplitude, frequency, and temperature change but also to a more detailed understanding of how the hysteresis shape of the material changes along the alteration of these parameters. The final model was calibrated using test data obtained from sweep amplitude tests over a range of frequencies and ambient temperatures and was able to accurately predict the dynamic performance of the dampers.

The cracking behaviors of rocks significantly affect their mechanical properties. In this paper, a digital analysis approach with X-ray Computed Tomography (CT) imagery is developed to investigate the cracking and mechanical behaviors of rocks. The damage ratio, integrity, and porosity of rocks subjected to triaxial compression are firstly defined based on X-ray CT image and the pixel coordinate system. Then, the evolution process of two-dimensional (2D) and three-dimensional (3D) cracks are studied via 2D CT images and reconstructed 3D fracture models, respectively. Finally, the stress–strain relationship of rocks is simulated by converting the reconstructed models to the finite-element (FE) models. The results show that the rock damage ratio, integrity, and porosity are good factors to describe the cracking behaviors, in which the evolution process of cracks is divided into five stages including: (1) the compaction of initial fissures; (2) the initiation and propagation of microcracks; (3) microcracks coalescence, i.e., the formation and stable propagation of macrocracks; (4) the unstable propagation of macrocracks; and (5) the complete failure of rock samples. The numerical stress–strain curves are in good agreement with the experiment data.

To explore the effects of holes and other defects on the dynamic mechanical properties of frozen soil under impact loading, frozen soil samples with three types of circular hole defects and different apertures were developed, and a dynamic compression experiment was performed with a split Hopkinson pressure bar (SHPB) device. The results indicated that the existence of holes weakens the dynamic compressive properties of frozen soil. The effects of temperature and holes on the defective samples were evident. The trend observed in the stress–strain curve was consistent with that observed in the samples without holes. The SHPB experiment using frozen soil samples with prefabricated holes was numerically simulated using LS-DYNA software and the Holmquist–Johnson–Cook material model; the simulation results showed good agreement with the experimental results. Using the postprocessing software LS-Prepost, the specific failure mode of the samples with holes was identified. The samples were found to have an X-type shear failure that was consistent with the theoretical research and the same as the failure rule of rock with holes. The dissipation energy per-unit volume was used to represent the energy-dissipation efficiency of the sample in the experiment. As the failure of a sample with holes led to more cracks, the energy-dissipation rate of a sample with holes was higher than that of a sample without holes, and it increased as the aperture increased.

Structural reliability analysis involving highly nonnormally distributed performance functions or relatively small failure probabilities is still a challenging problem in engineering practice. To overcome these problems, this paper developed the moment method combined with Box–Cox transformation. A new criterion is proposed to select the optimal Box–Cox transformation parameter that makes the transformed performance functions approximately normally distributed. This criterion was established based on the minimum distance between the pair of the skewness and kurtosis of the transformed performance function and that of a normal random variable, in which the statistical moments of the transformed performance function are evaluated from the point-estimate method. The failure probability was evaluated using a third-order moment reliability index. The accuracy and efficiency of the proposed method were demonstrated through several numerical examples, including structural reliability analysis with correlated random variables; stochastic processes; and nonnormal, nonlinear, and implicit performance functions.