Journal of Engineering Mechanics

A new micromechanical model is developed for the prediction of the elastic properties of composite materials with embedded spherical multicoated inhomogeneities of various sizes and types. The model is based on the $n+1$ phase model and the Mori–Tanaka homogenization. The model is capable of treating each coated spherical inhomogeneity individually, including specific attributes such as particle size and multiple mechanical phases. The accuracy of the model is assessed by comparing it with classical bounds and an analytical model from the literature. The results of the model are also compared with experimental data for the case of a three-phase composite material. The influence of mechanical properties and volume fraction of various constituents on the bulk elastic properties is also studied for the case of multiphase complex materials.

Non-Gaussian processes beset many aspects of structural engineering analysis. To estimate non-Gaussian processes, various third-order Hermite polynomial models have been proposed and widely applied. Different forms of expressions have been proposed for hardening and softening processes in existing Hermite polynomial models, which makes them inconvenient to implement. Furthermore, these models are either too simple to ensure accurate results or too complicated to implement conveniently. Thus, a unified third-order Hermite polynomial model that achieves a good balance between accuracy and convenience for both hardening and softening processes is proposed in this study. Explicit expressions for translations of the marginal distributions between the non-Gaussian and Gaussian processes using the proposed Hermite polynomial model are deduced, and the applicable ranges are provided. The accuracy of the proposed model is demonstrated by comparing the coefficients and estimated moments with those obtained from the moment-matching method. Furthermore, the application of the proposed model in evaluating first passage probability, analyzing fatigue damage, and estimating peak factors of non-Gaussian wind pressure coefficient histories is demonstrated with numerical and practical examples.

A general framework is proposed to incorporate rate and time effects into bounding surface (BS) plasticity models. For this purpose, the elasto-viscoplasticity (EVP) overstress theory is combined with bounding surface modeling techniques. The resulting constitutive framework simply requires the definition of an overstress function through which BS models can be augmented without additional constitutive hypotheses. The new formulation differs from existing rate-dependent bounding surface frameworks in that the strain rate is additively decomposed into elastic and viscoplastic parts, much like classical viscoplasticity. Accordingly, the proposed bounding surface elasto-viscoplasticity (BS-EVP) framework is characterized by two attractive features: (1) the rate-independent limit is naturally recovered at low strain rates; and (2) the inelastic strain rate depends exclusively on the current state. To illustrate the advantages of the new framework, a particular BS-EVP constitutive law is formulated by enhancing the modified Cam-clay model through the proposed theory. From a qualitative standpoint, this simple model shows that the new framework is able to replicate a wide range of time/rate effects occurring at stress levels located strictly inside the bounding surface. From a quantitative standpoint, the calibration of the model for overconsolidated Hong Kong marine clays shows that, despite the use of only six constitutive parameters, the resulting model is able to realistically replicate the undrained shear behavior of clay samples with OCR ranging from 1 to 8, and subjected to axial strain rates spanning $0.15\%/\mathrm{h}$ to $15\%/\mathrm{h}$. These promising features demonstrate that the proposed BS-EVP framework represents an ideal platform to model geomaterials characterized by complex past stress history and cyclic stress fluctuations applied at rapidly varying rates.

This paper theoretically demonstrates two aspects of a generalized heat conduction model with memory-dependent derivatives. The characteristics of transient effects in an isotropic, thermoelastic medium were analyzed in terms of memory-dependent thermoelasticity theory. The Lord–Shulman (LS) model gives an upper bound of thermal disturbances in a memory-dependent generalized thermoelasticity model. For numerical implementation, a one-dimensional semi-infinite medium with one end subjected to a transient load was considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic numerical inverse Laplace transform (NILT) were adopted. Parameter studies were performed to evaluate the effect of the kernel function and time delay. An appropriate Lyapunov function, which is a significant scheme to study numerous qualitative properties, is proposed.

The heat transfer problem is often considered to be the kernel of a fire resistance analysis. In fact, one- or two-dimensional closed-form solutions have long laid the foundation for an engineer’s understanding of the temperature distribution within a structural element exposed to fire. Although many closed-form solutions of the thermal problems for structural members in buildings exist, the literature is surprisingly thin for bridge structures—and even more so for suspension bridge structures. This paper addresses that sparsity by presenting a generalized approach for the formulation and solution of the heat transfer problem for a suspension bridge main cable exposed—either partially or completely—to fire. The approach first normalizes and then nondimensionalizes the problem. It then divides the resulting generalized time-dependent heat equation with spatially dependent boundary conditions into a steady-state and transient problem and subsequently solves each piece with a classic separation of variables technique. The functionality of the solution is assessed by performing both an error analysis and a computational time comparison with numerical results for three verification problems.

In this paper, a probabilistic framework for constructing a dynamic modified model for RC columns was developed based on dynamic loading test results and the Bayesian updating method. The influences of strain rate on the mechanical behaviors of RC columns were investigated by analyzing the experimental data obtained from dynamic loading tests. The basic equations of dynamic modified models for RC columns in terms of yielding strength, ultimate strength, pre-yielding stiffness, and ductility coefficient were established based on the Bayesian updating theory. Posterior distributions of the unknown model parameters were estimated using the Markov chain Monte Carlo (MCMC) algorithm, which provided insight into the mechanism of the dynamic effect on RC structural members. By comparing the predicted results with available experimental data, the accuracy and effectiveness of the proposed models were verified. It was found that the Bayesian-based models can obtain more-accurate predictions of the skeleton curve of RC columns under both uniaxial and biaxial dynamic loadings. Moreover, the superiorities of the Bayesian-based models over the non-Bayesian models were presented through quantitative comparison. The presented approach provides a valuable assessment of the dynamic behaviors of RC structural members, which can be used to improve the accuracy of the seismic response predictions of RC structures.

Rigid barriers are commonly used as defense measures in hilly areas to contain falling boulders and landslide debris, and the sliding displacement of these barriers is a key design consideration when space is limited. A new displacement-based model in the form of a closed-form solution is introduced in this paper to estimate the amount of sliding displacement that a barrier undergoes following a boulder impact. The model was derived based on the principles of energy and momentum conservation, and the derivations were presented. Laboratory tests were conducted to validate the analytical model, and the results consistently matched the analytical results for different impact velocities. Finite-element modeling was subsequently carried out on a real-scale barrier in Hong Kong to verify the scale-independent nature of the model. A parametric study was also carried out to investigate the effect of basal friction on the sliding behavior of the barrier. The results revealed that the effect of friction diminishes with increasing barrier:boulder mass ratio.

This paper presents a macroscopic constitutive model that is able to reproduce the uniaxial transformation ratcheting behaviors of the superelastic shape memory alloy (SMA) undergoing cyclic loading. A cosine-type phase transformation equation with the initial martensite evolution coefficient that helps to predict the residual martensite accumulation and the nonlinear features of the hysteresis loop with a small number of material parameters is established to describe the phase transformation behaviors of the SMA undergoing cyclic loading. The proposed model simultaneously takes into account the evolution of transformation-induced plastic strain during cyclic loading. The applied loading level and asymmetric tensile and compressive behavior of the SMA on transformation ratcheting are also considered in the proposed model. The evolutions of transformation ratcheting, transformation-induced plastic strain, and transformation stresses are constructed as the function of the accumulated residual martensite volume fraction. The simulated results are compared with the experimental results to show the validity of the proposed model in transformation ratcheting.

In this study, a novel composite time integration method is proposed for more accurately and efficiently solving typical structural dynamic problems. In this method, the second-order accuracy is ensured for dynamic problems. First, the stability, accuracy properties, local truncation error, and global error are analyzed and compared with available state-of-the-art methods in the literature. Then, three sets of parameters are recommended and discussed, and optimization of these parameters results in a high accuracy and efficiency of the proposed method. Finally, three classical examples with high-frequency vibrations, where a large ratio of the time step size to the period is adopted, are presented to demonstrate the accuracy, efficiency, and applicability of the proposed method.

Four-point bending tests have been a staple in many structural engineering experiments as a reliable way of assessing the bending resistance of circular hollow sections, tubes, and cylindrical shells, and they continue to be widely performed. However, relatively little attention appears to have been paid to quantifying the effects of different boundary conditions on the test outcome. In particular, the restraint or freedom given to the cross section at the ends of a specimen to ovalize can have a significant impact when the specimen is in an appropriate length range. Ovalization is an elastic geometrically nonlinear phenomenon that is known to reduce the elastic bending resistance by as much as half in long tubes or cylinders. This paper presents a short distillation of some recent advances in understanding the buckling of cylindrical shells under uniform bending, identifying the strong influence of cylinder length on cross-section ovalization. A sample set of three-dimensional load application arrangements used in existing four-point bending tests was simulated using finite elements, allowing an assessment of the differences caused by prebuckling ovalization and its effect on the tested bending resistance. The study is limited to elastic behavior to identify the effect of ovalization alone in reducing stiffness without material nonlinearity. The outcomes demonstrate that maintaining circularity at inner load application points by appropriate stiffening has a significant effect. With freedom to ovalize, a significant reduction in stiffness occurs, leading to much lower bending resistance at buckling than may be achievable in practical applications.

Temperature change after formation commonly results in thermal residual stress in multilayered structures due to the different thermal and mechanical properties of each layer. In this paper, a three-dimensional (3D) elastic model is developed to study the residual stress and opening-mode fractures (OMFs) in a multilayered structure consisting of arbitrary number of layers under temperature change. The general solution of displacement field in the multilayered structure is derived by solving the elastic boundary value problem. In order to verify the proposed model, the elastic field in the advanced polymeric solar reflectors that consist of four layers is solved by applying the present model and compared with the finite-element (FE) simulation. In addition, parametric studies are conducted to investigate the effect of the thickness ratio between each layer on the accuracy of the developed model. Based on the obtained elastic field, the fracture energy release rate (ERR) in the surface layer of the advanced polymeric reflector is obtained and used to study the fracture initiation, infilling, and saturation successfully.