Journal of Engineering Mechanics

In this work, a plane-stress element is proposed for the elastoplastic dynamic analysis of two-dimensional structures exhibiting hysteretic behavior. The constant-strain triangular element formulation for the elastic case is modified by introducing the Bouc-Wen hysteretic model, properly defined in the 2D stress-strain space. Solutions are obtained by simultaneously solving two sets of governing equations, namely the global equilibrium equations and the local constitutive equations, using a predictor-corrector differential equation solver. In following the proposed method, the linearization of the constitutive relations usually performed in step-by-step solution approaches is avoided. The proposed element is capable of modeling cyclic induced phenomena such as stiffness degradation and strength deterioration. Furthermore, the solution method implemented improves the accuracy of the results without increasing the computational cost of the analysis. Examples are presented which demonstrate the efficiency of the proposed approach. The method can be extended to other types of finite elements by properly incorporating the nonlinear constitutive behavior into their stiffness matrices.

The rocking motion of a solid block on a moving deformable base is a dynamic problem that, despite its apparent simplicity, involves a number of complex dynamic phenomena such as impacts, sliding, geometric and material nonlinearities and, under some circumstances, chaotic behavior. For this reason, since the first model proposed by G.W. Housner in 1963, a number of alternative models have been proposed for its mathematical simulation. In this work, two new models are developed for the simulation of a rigid body experiencing a 2D rocking motion on a moving deformable base. The first model, the concentrated springs model, simulates the ground as tensionless vertical springs with vertical dampers placed at each of the two bottom corners of the body, whereas the second, the Winkler model, simulates the ground as a continuous medium of tensionless vertical springs with vertical dampers. Both models take into consideration sliding (with the use of both a penalty method and an analytical formulation for friction) and uplift and both are geometrically nonlinear. The models are used for simple free vibrational problems in which the effects of the ground deformability, sliding, and uplift are noted. In addition, the stability diagram for various parameters of the system, under excitation by ground motions that correspond to one full cycle sine pulses with varying amplitude and frequency, is created. The behavior of the two models is discussed and compared with the classic theory proposed by Housner.

An Anisotropic Critical State Theory (ACST) for granular media is presented, which accounts for the role of anisotropic fabric at critical state. It enhances the requirements of critical values for the stress and void ratio of the classical Critical State Theory (CST) by an additional requirement of critical value for an appropriate measure of fabric-anisotropy. A fabric tensor and its evolution toward a critical value, norm-wise and direction-wise, is introduced motivated by micromechanical and experimental studies. On the basis of a scalar-valued fabric-anisotropy variable relating the evolving fabric tensor to the loading direction, a dilatancy state line is defined in the void ratio—pressure plane which determines a dilatancy state parameter $\zeta$ that characterizes the contracting or dilating trends of the current state. When the fabric-anisotropy variable reaches its critical state value, the dilatancy state line becomes identical to the critical state line and the $\zeta$ identical to the well-known state parameter $\psi$. An immediate corollary is the uniqueness of the critical state line, for which a thermodynamic proof is provided on the basis of the Gibbs condition. Static liquefaction is obtained when $\zeta =0$ with the stress ratio reaching its critical value but not the void ratio and the fabric. Simulations of anisotropic material response by a triaxial model are used to illustrate the effectiveness of the novel ACST.

The time-domain evaluation of the frequency-dependent dynamic stiffness was studied, and some transform methods were proposed. Although various kinds of stiffness have been well-transformed by these methods, some problems remain. In this paper, the following two problems are studied. First, the relationship between the proposed transform methods and Duhamel’s integral is studied to understand the meaning of the two series of impulse responses obtained by the methods. Next, the time-domain transfer function, obtained by the transform of frequency-domain transfer function, is shown to expand the applicability of the methods. Seismic response values are easily calculated in the time domain using the function without FFT. The efficiency of the function is confirmed with a practical example problem.

A new finite-element framework for lower-bound limit analysis of reinforced concrete beams, subjected to loading in three dimensions, is presented. The method circumvents the need for a direct formulation of a complex section-force-based yield criterion by creating a discrete representation of the internal stress-state in the beam. The yield criteria are formulated and applied on a stress-state level. The stress-state is decomposed to concrete and reinforcement stresses, and separate yield criteria are applied to each component. Simple limits are used on the reinforcement stresses, and a modified Coulomb criterion is applied to the concrete stresses. The modified Coulomb criterion is approximated using second-order cone programming for improved performance over implementations using semidefinite programming. The element is verified by comparing the numerical results with analytical solutions.

The stress-strain relation of cement binder is age-dependent and so is the behavior of mortar. In this study, we conducted a concurrent experimental and theoretical investigation into the effect of material age on the properties of both cement binder and mortar. First the stress-strain curves of the binder were measured over a wide range of aging time from 7 days to 18 months. Two types of binder—one with the cement paste alone and the other with the fly ash/cement combination—were chosen in the tests. The test results were simulated with a modified, age-dependent Burgers rheological model. Then measured were the stress-strain curves of the mortar that contains the same types of cement at three levels of aggregate volume concentrations: $c_1=29$, 38, and 49%. A micromechanics-based composite model making use of the secant-moduli was then introduced to predict the age-dependent behavior of mortar at various aging times and aggregate concentrations. Direct comparison between the measured data and the composite predictions is found to be in close agreement. It suggests that the proposed micromechanics model could be a viable approach to the estimate of age-dependent constitutive relations of mortar.

The seismic risk assessment of a structure in performance-based design (PBD) may be significantly affected by the representation of ground motion uncertainty. In PBD, the uncertainty in the ground motion is often represented by a probabilistic description of a scalar parameter, or low-dimensional vector of parameters, known as the intensity measure (IM), rather than a full probabilistic description of the ground motion time history in terms of a stochastic model. In this work, a new procedure employing relative sufficiency measure is introduced on the basis of information theory concepts to quantify the suitability of one IM relative to another in the representation of ground motion uncertainty. On the basis of this relative sufficiency measure, several alternative scalar- and vector-valued IMs are compared in terms of the expected difference in information they provide about a predicted structural response parameter, namely, the seismically induced drift in an existing reinforced-concrete frame structure. It is concluded that the most informative of the eight considered IMs for predicting the nonlinear drift response are two scalar IMs and a vector IM that depend only on the spectral ordinates at the periods of the first two (small-amplitude) modes of vibration.