Journal of Engineering Mechanics

The behavior of material nonlinearity with nonassociative plastic flow is frequently analyzed for structures made of soil and rock. It is known that for nonassociated plasticity, the elastoplastic tangential stiffness tensor (matrix) is nonsymmetric. In the FEM, this causes inconvenience for solving a system of equations using the Newton-Raphson solution procedure. In this paper, a mathematical transformation was derived for converting the nonsymmetric tangential stiffness tensor (matrix) into a symmetric tensor such that the global system of equations become unconditionally symmetric. A detailed step-by-step procedure of a stress update algorithm using the tangential stiffness method is elaborated in this paper. The paper also compares the results of the tangential stiffness method with those of the initial stiffness method using an illustrative tunnel problem for associative and nonassociative flow conditions and shows the efficacy of the proposed transformation in elastoplastic problems.

Time integration is the most versatile tool for analyzing semidiscretized equations of motion. The responses are approximations, with deviations from the exact responses mainly depending on the integration method and the integration step sizes. When repeating the analyses with smaller steps, the responses generally converge to the exact responses. However, the convergence trends are different in linear and nonlinear analyses. Whereas in linear analyses, by decreasing the sizes of integration steps, the errors decrease with a rate, depending on the orders of accuracy, in nonlinear analyses, the change in errors might be unpredictable. The main reason is the inconsistency between the integration steps sizes and the residuals of nonlinearity iterations. In this paper, based on careful selection of nonlinearity tolerances, a methodology and a method to overcome this inconsistency for semidiscretized systems with piecewise linear behavior are introduced. When the responses converge, except for systems with very complex behaviors, the proposed method leads to proper convergence, with tolerable computational costs. In addition, by implementing the proposed method, more reliable error estimations can be expected from convergence-based accuracy controlling methods.

Based on asymptotic considerations, this paper develops an improved approximate formula for estimating the relaxation function from the given compliance function of concrete, which is considered as aging, linearly viscoelastic material. Compared with the formula developed in 1979 by Bažant and Kim, the new formula prevents any violation of the thermodynamic requirement of nonnegativeness of the relaxation function. It is significantly more accurate for long-time relaxation of concrete loaded at a young age, and, for this reason, it is particularly useful for compliance functions that correctly describe multidecade creep, which is the case for model B3 compliance function (a 1995 international RILEM recommendation) and not, for example, for the compliance functions of the American, European, Japanese, and Canadian standard recommendations, for which the benefit is smaller. The main application of the new formula is to evaluate the aging coefficient of the age-adjusted effective modulus method (AAEM) from the compliance function specified by the standard recommendation. The AAEM, developed in 1972 at Northwestern University and embodied in most standard design recommendations including those of the American Concrete Institute (ACI) and the Fédération internationale du béton (fib), provides an approximate estimate of the creep effects in structures according to the principle of superposition, which itself is a simplification neglecting nonlinear and diffusion effects.

The finite-element methodology is presented to evaluate the energy absorption performance of staggered triangular honeycombs under in-plane crushing loadings at impact velocities of 50–300 m/s. The minimum dynamic cushioning coefficient is proposed to characterize the maximum energy absorption efficiency of staggered triangular honeycombs. When all configuration parameters are constant, the energy absorption per unit volume is proportional to the square of the impact velocity; for a given impact velocity, the energy absorption per unit volume is related to the ratio of the cell wall thickness to the edge length by a power law and to the expanding angle by complicated analytical equations. The maximum energy absorption efficiency is insensitive to the impact velocity. Only for the smaller ratio of the cell wall thickness to the edge length does the maximum energy absorption efficiency increase with the increasing expanding angle. At a given impact velocity there is a threshold ratio of the cell wall thickness to the edge length. The maximum energy absorption efficiency decreases abruptly when the ratio is larger than the threshold. The threshold ratio is approximately equal to 0.04.

Laboratory tests, including splitting tension, three-point bending, and direct shear tests, were conducted on polymer cement mortar (PCM)-concrete composite specimens with various degrees of interface roughness ($R_a$). The PCM-concrete bond strength, fracture energy, and fracture surface were investigated qualitatively. The failure mode and the condition of the fracture surface significantly affected the interface bond strength and fracture energy. The bond strength and fracture energy were found to increase with increasing interface roughness until the fracture location shifted from the PCM-concrete interface to within either the PCM or the concrete. The interface roughness has a greater influence on the interface fracture energy and the flexural strength than on the tensile and shear strengths. Considering the single mode (Mode I or Mode II) bond and fracture properties, as well as retrofitting costs, a roughness index of approximately 1 mm ($0.9\le R_a\le 1.1\mathrm{mm}$) is proposed as the optimum value of interface roughness, and the corresponding recommended treatment is water-jetting (WJ) to a depth of 2–2.5 mm. Finally, an interfacial tension softening model that takes into account the effects of fracture energy, tensile strength, and failure mode is presented.

An electronic speckle pattern interferometry (ESPI) system, which delivers high-resolution displacement data from fringes that are formed by the subtraction of laser speckle patterns, was constructed to study fracture initiation in a quasi-brittle material. Mode I opening and Mixed-Mode I and II fracture experiments were performed with a homogeneous, fine-grained (0.1–0.8 mm grain size) sandstone using the three-point bending test. Specimens were notched at various lengths and positions of the beam edge to produce the desired loading condition, with $K_{\mathrm{II}}/K_{\mathrm{I}}=\text{0}-13\%$. The experimental results indicate that the length of the localized damage zone at peak load for Mode I fracture is 6–7 mm, which is about 10 times the (largest) grain size. From the mixed-mode loading tests, the zone length at peak load increased to 10–12 mm, and the length was more or less constant for $K_{\text{II}}\text{/}{K}_{\text{I}}=5-13\%$. ESPI also provided detailed information on the horizontal displacement profiles along the damage zone. For center notch specimens at peak load, the horizontal (opening) displacement at the notch tip was 40 $\mu$m, which can be interpreted as the critical opening displacement if the damage zone is fully formed at peak. For mixed-mode specimens, the critical horizontal displacement at peak load is 60–80 $\mu$m, but the vertical displacement is needed to resolve the critical opening and sliding components.

Innovative initial elastic strain energy–based coupled elastoplastic hybrid isotropic damage and healing models for partially saturated soils have been developed and implemented for numerical simulation of two-dimensional earth-pushing processes. A class of elastoplastic constitutive damage-healing models, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy–based formulation. In particular, the change of effective stress caused by matric suction in the formulation is considered, and the governing incremental damage and healing evolutions are coupled and characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence. Further, plastic flow is introduced by means of an additive split of the stress tensor. In this innovative formulation, two characteristic energy norms of the tensile and compressive strain tensors, respectively, are introduced for the corresponding damage and healing mechanisms. By incorporating a micromechanics-motivated damage characterization (${\mathbf{P}}^{+}$) and a healing characterization (${\mathbf{P}}^{-}$), the proposed model and computational algorithms have been implemented to demonstrate the significant flexibility on numerical simulation of earth-pushing processes. Completely new computational algorithms are systematically developed based on the two-step operator splitting methodology. The elastic-damage-healing predictor and the plastic corrector are implemented within the existing reproducing kernel particle method mesh-free codes. A numerical example under soil pushing is presented to illustrate the effect of matric suction for partially saturated soils or granular materials.

Traditional methods of using surrogate data to test for linearity of time-series data can be extended into the time-frequency domain to test for stationarity. Surrogates are time series that are created directly from the original dataset through manipulation and seek to replicate important properties of the original dataset. By comparing the original signal to the surrogates, additional structure in the original dataset not explained by the replicated properties may be revealed. The surrogates used for the purpose of testing stationarity are stationarized versions of an original signal that have the same Fourier amplitudes, but have randomized phases. Wavelet analysis is used in this method to transform the signals into the time-frequency domain and wavelet scalograms are used to quantitatively compare the original signal to the stationarized surrogate signals. Methods introduced in previous research compare the local and global spectral features of the surrogate signals with the local and global spectral features of the original signal to evaluate the stationarity of the signal as a whole. These methods are compared with a perceived new method, introduced here, that uses the surrogate-signal scalograms, which should contain no meaningful nonstationarity, to filter-out stationary portions of the original signal and noise, revealing where nonstationarity may be occurring within the signal. The methods are tested on a diverse set of generated signals as well as data from windstorms such as hurricanes and thunderstorms/downbursts, which may contain strong nonstationary features characterized by rapid changes in wind speed and direction. While several of the methods presented in previous research show good results with specific types of nonstationarity present, it is shown that the new technique of filtering out stationarity is better able to evaluate signals that contain many sources of nonstationarity.

A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable.

Hybrid simulation combines numerical simulation and experimental testing in a loop of action and reaction to capture the dynamic behavior of a structure. With an extended time scale, convergence of the desired displacements or forces can be assured in each actuator connected to the experimental component before advancing to the next time step. However, when the rate-dependent behavior of an experimental component is of interest, the hybrid simulation must be conducted in real time [i.e., real-time hybrid simulation (RTHS)]. In RTHS, the dynamic behavior of the loading system (i.e., actuators, controllers, and computers) is directly introduced into the RTHS loop. These dynamics consist of both time delays and frequency dependent time lags. At the same time, the phenomenon of control-structure interaction leads to a coupling of the dynamic behavior of the actuators and the structure. Traditional actuator control approaches for RTHS compensate for an apparent time delay or time lag rather than address the actuator dynamics directly. Moreover, most actuator control approaches focus on single-actuator systems. The RTHS control approach proposed herein directly addresses actuator dynamics through model-based feedforward-feedback control. Capturing the dynamic coupling between the actuators ensures accurate control for multiactuator systems. The proposed approach is illustrated through numerical simulation for a 3-story building with multiple actuators to provide control during RTHS.

In the first part of this paper, an exact analytical solution in closed form for linear long-wave reflection by a submerged idealized breakwater or trench with various curvilinear slopes is given. The solution obtained finds almost all previous long-wave analytical solutions for wave reflection by idealized bathymetries to be its special cases, including the wave reflection by an infinite step, a continental shelf with a parabolic slope, a continental shelf with a linear slope, a rectangular obstacle, an obstacle of general trapezoidal shape with linear slopes, and a trench of general trapezoidal shape with linear slopes. In the second part, an exact analytical solution in the form of a Taylor series for linear long-wave reflection by a submerged quasi-idealized breakwater or trench is also constructed. It is shown by convergence analysis that the series solution converges in the entire physical domain. Based on the present analytical solutions, the reflection coefficients for long waves reflected by various breakwaters are calculated and the influence of the breakwater dimensions in the reflection effect is investigated. It is always found that the total reflection defined by the area under the reflection coefficient curve increases when the front and back slopes become steep. It is also found that the phenomenon of zero reflection for a symmetrical rectangular breakwater still remains for a general breakwater with curvilinear slopes as long as the bathymetry is symmetrical about the breakwater.