Journal of Engineering Mechanics

A generalized constitutive model based on hypoelastic theory is proposed to characterize the stress-strain relationship of plain concrete under monotonic and cyclic nonproportional loading. First, the existing hypoelastic incremental models are reviewed and some features of concrete behavior are described. The behavior of concrete is modeled using a normalized scalar damage parameter, the equivalent strain concept, and either the Willam-Warnke five-parameter or the Hsieh-Ting-Chen four-parameter failure surfaces. A new tensile strength criterion and a method for objective modeling of the postpeak compression state are derived. The important features of nonlinear behavior of concrete, such as the volumetric dilatation, the transition state from brittle-softening to ductile-hardening behavior, degradation of the elastic modulus under cyclic loading, and the postcrushing state are all represented by the proposed constitutive model. Comparison of the model predictions with laboratory tests support the validity of the proposed formulation. It is believed that the proposed constitutive relationships provide a good compromise between simplicity and accuracy for modeling plain concrete.

A boundary element model is presented for the computation of dynamic stiffnesses of strip foundations resting on or embedded in soils that are fluid-filled poroelastic and may also have single-phase viscoelastic zones. The two-phase behavior of the porous medium is represented according to Biot's theory. The interaction between the porous medium and the foundation or the zones of the soil that are viscoelastic is rigorously represented. The contact conditions between the soil and foundation can be pervious or impervious, welded or smooth. The technique is applied to the computation of dynamic stiffnesses of foundations on a saturated poroelastic half-space and on a saturated poroelastic stratum based on rigid or compliant bedrock. Stiffness components are computed and compared with existing results for a half-space and for a stratum. The effects of the properties of the porous medium, the kind of contact between soil and foundation, the depth of the porous stratum, and the compliance of the bedrock on the dynamic stiffnesses are examined. The technique presented in this paper is able to represent more general properties and geometries of the soil than do the existing approaches.

Based on three-dimensional elastic theory, three components of displacement are expanded by orthotropic series. A second-order ordinary differential equation set is then obtained that can be solved by Frobenius Method. Considering the effect of the fluid, we can get the frequency equation of nonaxisymmetric free vibration of orthotropic fluid-filled cylindrical shell with arbitrary constant thickness. Some examples are illustrated to compare results with those based on shell theory.

This paper presents relationships between the buckling loads determined using classical Kirchhoff plate theory and shear deformable plate theories. The latter theories considered are the first-order shear deformation plate theory of Reissner-Mindlin and the third-order plate theory of Reddy. The relationships are exact for isotropic, simply supported polygonal plates under an isotropic inplane load and resting on a Pasternak foundation. Using the relationships, buckling solutions of the Reissner-Mindlin and Reddy plate theories can be readily obtained from known buckling solutions of the Kirchhoff plate theory without the Pasternak foundation.

The behavior of power-law creeping materials in the form of thin films subject to plane strain and axisymmetric deformation is studied. Analytical calculations, finite-element analysis, and experimental studies are performed. Both the elastic and viscous behavior are investigated, and the effects of interfacial friction, compressibility, and delayed elasticity are discussed. Solutions are obtained for compression, shear, and combined compression with shear. The solutions provide a microscopic “flat-plate” viscous flow contact model for use in micromechanical models of particulates composites. It is concluded that for thin films the elastic component of the material behavior can be modeled accurately using Nadia's solutions for an elastic material, and that the nonlinear viscous component can be modeled well by assuming unidirectional flow in a uniform passage. These two solutions can be combined into a nonlinear Maxwell model that describes the contact behavior accurately, for small or large strains. Finally, the creep response of a plane-strain, power-law viscous contact under combined compression and shear can be approximated by an elliptical function in terms of compressive and shear stresses or strain rates.

Fracture mechanics is very often employed in analyses of cracked structural components. We present here another technique that is based on the equivalence between a crack, its process zone, and a distribution of damage. It is a simplified method aimed at approximating the distribution of damage around an existing crack. This approximation is based on the analysis of localization with a nonlocal damage model. Finite-element calculations on a compact tension concrete specimen for several initial crack lengths are presented and compared with experiments. The method is shown to yield errors less than 20% on the prediction of the load reduction factor as a function of the initial crack length. The method is also extended to the prediction of the response of fiber-reinforced components with initial damage. The response of cracked fiber-reinforced concrete (FRC) beams is computed and compared with the results of original experiments, where the loading conditions that created the initial crack are different from those leading to failure.

In this paper an algorithm is implemented for the control of uncertain nonlinear dynamical systems. The control algorithm is adaptive and consists of two phases. First, a system identification phase is implemented to develop a predictive model of the system based on its observed behavior. Second, a controller is designed to steer the predicted system response into a desired configuration. The control strategy to be presented in this paper is related to the well-known concepts of sliding mode control and variable structure control. Furthermore, the implementation of this control strategy utilizing smart materials is also addressed. Numerical examples are presented for the trajectory tracking and stabilization of uncertain nonlinear dynamical systems. Control strategies based on externally powered actuators and adaptive components are considered.

In civil engineering, the design of active vibration control systems for structures subjected to earthquake excitation is usually done using linear-quadratic optimal control theory. However, when this theory is applied to a system with an external forcing function, the function must be either neglected, known a priori, or treated as white noise. If it is treated as white noise, the control is optimized for steady-state response. For seismic analyses of structures, these three assumptions—that the earthquake input is known in advance, is neglected, or is white noise—are questionable. This represents a serious deficiency in using standard methods of linear optimal control for reducing structural vibrations under seismic loading. This paper presents a new method of addressing the issue of including the earthquake-type excitation explicitly in the development of control systems, by designing feedback and feedforward controllers whose gains are optimized by training on an ensemble of earthquakes. Two different control strategies are presented: in the first, the controller is composed of a state feedback term only (closed loop); in the second, a control term proportional to the external excitation is fed forward (open loop) in addition to the closed loop term. The development of the controller follows the general formalism developed by Kabamba and Longman (1981, 1983) for the design of optimal controllers of arbitrary prescribed order with quadratic cost functionals. In this formalism, the gradients of the cost functional are obtained in explicit form and involve Liapunov equations. The results of this study indicate that inclusion of the forcing function explicitly in the development of the controller provides better results than the standard Riccati solution and drastically reduces the peak structural response.

An intricate universal superstructure in bifurcation sets and routes to chaos of a nonlinear moored ocean system subjected to monochromatic wave excitations are investigated analytically and demonstrated numerically in detail herein. System nonlinearities include complex geometric restoring force and coupled fluid-system exciting forces. Primary and secondary resonance regions are identified by employing variational analysis techniques for local stability. Tangent and periodic doubling bifurcations are examined to reveal the underlying intricate superstructure. Numerical results of this complex system uncover a steady-state superstructure in the bifurcation sets that exhibit a similar bifurcation pattern of coexisting solutions in the subharmonic, ultraharmonic, and ultrasubharmonic domains. Within this superstructure it is illustrated that strange attractors appear when a period doubling sequence is infinite, and when abrupt changes in the size of an attractor occur near tangent bifurcations.

A new physical theory and constitutive model for the effects of long-term aging and drying on concrete creep are proposed. The previously proposed solidification theory, in which the aging is explained and modeled by the volume growth (into the pores of hardened portland cement paste) of a nonaging viscoelastic constituent (cement gel), cannot explain long-term aging because the volume growth of the hydration products is too short-lived. The paper presents an improvement of the solidification theory in which the viscosity of the flow term of the compliance function is a function of a tensile microprestress carried by the bonds and bridges crossing the micropores (gel pores) in the hardened cement gel. The microprestress is generated by the disjoining pressure of the hindered adsorbed water in the micropores and by very large and highly localized volume changes caused by hydration or drying. The long-term creep, deviatoric as well as volumetric, is assumed to originate from viscous shear slips between the opposite walls of the micropores in which the bonds or bridges that cross the micropores (and transmit the microprestress) break and reform. The long-term aging exhibited by the flow term in the creep model is caused by relaxation of the tensile microprestress transverse to the slip plane. The Pickett effect (drying creep) is caused by changes of the microprestress balancing the changes in the disjoining pressure, which in turn are engendered by changes of the relative humidity in the capillary pores. Numerical implementation, application, and comparison with test data is relegated to a companion paper that follows in this issue.

This paper presents a numerical algorithm for the microprestress-solidification theory developed in a companion paper and verifies this theory by comparisons with typical test data from the literature. A model for cracking is incorporated in the algorithm.

In this paper, the basic transfer functions and time-response functions of linear phenomenological models are revisited. The relation between the analyticity of a transfer function and the causality of the corresponding time-response function is extended for the case of generalized transfer functions. By using the properties of the Hilbert transform and the associated Kramers-Kroning relations it is shown that transfer functions that have a singularity at ω= 0 in their imaginary part should be corrected by adding a delta function in their real part. This operation ensures that the resulting time-response function is causal and is consistent with the theory of generalized functions. Accordingly, the transfer functions of classical viscoelastic models presented in standard vibration handbooks are revised. Finally, the addition of a delta function in the impedance of the noncausal ideal hysteretic dashpot that has been proposed in the literature is discussed.

In this paper the “causal hysteretic element” is constructed and analyzed. The dynamic stiffness of the proposed hysteretic model has the same imaginary part as the “ideal” hysteretic damper, but has the appropriate real part that makes the model causal. The proposed model is constructed by requiring that the real and imaginary parts of its transfer functions satisfy the Kramers-Kroning relations. This condition ensures that the corresponding time-response functions of the proposed model are zero at negative times. The causal hysteretic element is physically realizable at finite frequencies, but is not definable at ω= 0. The behavior of the proposed model is analyzed both in frequency and time domain. It is shown that the causal hysteretic element is the limiting case of a linear viscoelastic model with nearly frequency-independent dissipation. Finally, the response of a mass supported by the causal hysteretic element is discussed.