Journal of Engineering Mechanics

This paper derives an approximate expression for the true Young's modulus of a solid circular cylinder under compression between two end blocks with friction, provided that the Poisson's ratio is known. The conventional method of evaluating the Young's modulus assumes that uniform stress and deformation fields exist inside the specimen. However, if friction exists between the loading platens and the end surfaces of the specimen, a correction factor must be applied to the apparent Young's modulus. A correction factor with calculable error is obtained through the use of the Prager-Synge function space concept. The amount of friction is quantified by proposing a measurable parameter to model partial slip conditions. Numerical results show that the correction factor increases with both the slenderness ratio and the Poisson's ratio; these observations agree qualitatively with Filon's classical result. For the cases of partial slip, tables are provided for quick calculation of the correction factor.

The paper describes beam elements with inelastic hinges capable of modeling softening due to damage in building frames under severe loadings. A condition for uniqueness on the element level is derived, and the behavior of the model is compared to analytical solutions of simple structures (a single column and a portal frame). An application to postpeak analysis of a multibay frame is presented. Depending on the beam-to-column stiffness ratio and on a certain ductility parameter, various failure modes can occur, ranging from distributed to highly localized ones. This leads to a special type of size effect on the peak load, which is assessed numerically and related to analytically derived solutions valid in extreme situations—the elastic limit and the plastic limit.

A versatile, nonstationary stochastic ground-motion model accounting for the time variation of both intensity and frequency content typical of real earthquake ground motions is formulated and validated. An extension of the Thomson's spectrum estimation method is used to adaptively estimate the evolutionary power spectral density (PSD) function of the target ground acceleration record. The parameters of this continuous-time, analytical, stochastic earthquake model are determined by least-square fitting the analytical evolutionary PSD function of the model to the target evolutionary PSD function estimated. As application examples, the proposed model is applied to two actual earthquake records. In each case, model validation is obtained by comparing the second-order statistics of several traditional ground-motion parameters and the probabilistic linear-elastic response spectra simulated using the earthquake model with their deterministic counterparts characterizing the target record.

The concept of localization during the postpeak of compressive strain softening is presented. To explore localization in compression, a feedback-control method using a linear combination of displacement and force that partially subtracts the elastic response of the specimen to give a stable feedback signal is used. Results are presented from two test series (45 and 90 MPa) that use this method to test cylinders with length-to-diameter ratios ranging from 2.0 to 5.5 It is shown that compression failure is in fact a localized phenomenon. The compressive fracture energy is divided into energy dissipated in the prepeak and the postpeak portions of the stress-deformation response. It is found that the amount of energy required to propagate the compression failure during postpeak is independent of length for this range of specimens. The compressive fracture energies are compared for the normal and high-strength concretes.

An analytical procedure is presented for interpreting resistance histories from three piezoresistance gauges in a plane at a “point” to uniquely determine the normal stress at that point for nonuniaxial strain loading. The response of the elements can be plastic, and the analysis is valid for unloading and reloading. The only restrictions are that the elements must be aligned with the principal directions of the flow field, and the coupling between matrix strains and gauge strains must be specified. The gauges' piezoresistance properties, constitutive properties, and the coupling relations form a set of highly nonlinear simultaneous equations that can be solved for the normal stress and in-plane strains. A computer program named PIEZOR3 performs this task. Finite-element calculations are used to generate resistance histories from which the original stresses and strains can be computed with PIEZOR3. The computational examples demonstrate the accuracy of the procedure and quantify the uncertainties in the resolved stresses arising from uncertainties in mechanical, piezoresistance, and strain-coupling parameters.

Analytic three-dimensional solutions are presented for the free vibration problems of initially stressed hybrid multilayered composite circular cylindrical shells. The shells consist of a combination of fiber-reinforced cross-ply and piezothermoelastic layers. The initial stresses are generated by either a temperature change and/or an electric field. Sensitivity coefficients are also evaluated and used to study the sensitivity of the vibrational response to variations in the different mechanical, thermal and piezoelectric material properties of the shells. Both the temperature change and the radial component of the electric field are assumed to have uniform distribution in each layer of the shells. A linear constitutive model is used, and the material properties are assumed to be independent of both the temperature and the electric field. The thermoelectroelastic response of the shell is subjected to time-varying displacements, strains, and stresses, and the free vibration response is studied. A mixed formulation is used with the fundamental unknowns consisting of the increments of the three transverse stress components and the three displacement components of the shell. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the axial and circumferential surface coordinates. A state space approach is used to generate the vibrational response and to evaluate the sensitivity coefficients. A sublayer method is used for evaluating vibration frequencies and their sensitivity coefficients. Numerical results are presented showing the effects of variation in the shell thickness, and the location of the piezothermoelastic layers on the vibration frequencies and their sensitivity coefficients.

Based on a microstructural approach, granular material can be represented by an equivalent continuum of the high-gradient type. The high-gradient model is used in this paper to study the effect of microstructure on the propagation of waves in granular material. The constitutive coefficients of the high-gradient continuum are expressed in explicit functions of interparticle stiffness. Based on the high-gradient model, a fourth-order partial differential equation is formulated for the wave propagation in granular medium. Hamilton's principle is employed to devise the additional boundary conditions involved in the differential equation. The differential equation is solved for wave propagation in a finite rod of granular material with specified boundary conditions. The present results show that the dynamic behavior of a rod of granular solid is very different from the behavior of a rod of classical continuum. The predicted phenomena are in agreement with the simulation results from discrete element methods and with the experimental observations from a chain of photoelastic disks subjected to an impact load.

Concrete is a highly heterogeneous multiphase material, and its constitutive and damage behavior has some very special characteristics. In this paper an elastoplastic constitutive relationship is proposed for damaged concrete materials based on a thermomechanically consistent mechanical model. The proposed relationship takes into account the interaction between volumetric and deviatoric inelastic deformation, hardening, anisotropic damage, unilateral effect of damage, and different failure modes. The validity of the proposed model is verified by comparing theoretical and experimental results of concrete subjected to triaxial stress histories with strain-controlled cyclic loading and unloading.

Existing theories of flow and contaminant transport in aquifers are either based on Monte Carlo simulations or small perturbation solutions of the governing stochastic partial differential equations, which limit the applications to cases of small variances in the physical parameters. In most cases the “smallness” is a subjective statement from the modeler or is forced by considering the logarithm of the random quantities. This article constitutes a preliminary attempt to reanalyze the problem of flow and contaminant transport in a hypothetical heterogeneous aquifer without the usual assumptions of small perturbation, logarithmic transformation, a specific probability law, and disregard for the underlying hydrologic problem. Statistical properties of the pore velocity are derived from the inherent ground water flow problem; a non-Fickian dispersion equation is derived by assuming two scales, a small and a large one; and a solution of the dispersion equation is obtained. A general analytic procedure, the decomposition method is used in the solution of the flow and dispersion equations. Finally, some comparisons with existing results are presented.

It appears from macroand microexperiments that the essential response feature beyond the secondary stage of rock salt creep is characterized by the evolution of localized damage that results in the formation and propagation of macrocracks. To predict the creep response of rock salt, a modeling framework with a corresponding integration scheme is developed based on thermodynamic restrictions. The jump forms of conservation laws are used to identify the transition from continuous to discontinuous failure modes. To obtain a continuum tangent stiffness tensor for bifurcation analyses, a simple creep model is formulated from the modeling framework by combining a viscoplastic part with an implicitly rate-dependent damage part. Sample problems are considered to illustrate the proposed procedure.

Fracture mechanics was used to evaluate failure of the rib/skin connection of composite “isogrids.” The energy derivative method was used to determine the strain energy release rate (G) using a general purpose finite-element (FEM) program with an orthotropic material model. Flexure tests were conducted to observe when rib/skin interface fractures propagate, and the results were correlated with the FEM-based fracture mechanics model. A laser interferometry technique, electronic shearography was used to monitor crack propagation during the flexure tests. Environmental scanning electron microscopy (ESEM) was used to understand the micromechanical aspects of fracture. Variation of the fiber volume fraction, rib thickness, and the presence of weak shear zones were found to be critical to the failure process. The paper explores the concepts of linear elastic and nonlinear fracture as applicable to these graphite/epoxy composite structures. This study provides the designers and users of the isogrid with a methodology for quantifying structural degradation as a function of the rib/skin disbond.