Journal of Engineering Mechanics

The volumetric creep of loose granular materials, in absence of pore fluid pressure, is modeled as a stochastic process of diffusion-convection for excess porosity under sustained, applied loading. The analogy of the underlying concepts, with the theory of sedimentation in Brownian motion, and differences with the earlier contribution of Marsal (1965) are discussed. The analytical formulation and numerical solution are presented for a 1D compression with finite strain and moving boundary surface. The results represent the time evolution of the spatial distribution of the material porosity and the rate of settlement. The compression versus time relationship is normalized in dimensionless form to facilitate the determination of the governing equation coefficients from test data. Examples of determination and comparisons with the model response are presented. According to the model, final settlement is reached asymptotically with equilibrium porosity. At transient states, the spatial distribution of porosity is not necessarily uniform, even when both initial and final distribution are uniform.

The critical excitation method is promising as a robust method for accounting for inherent uncertainties in predicting forthcoming earthquake events and for constructing design earthquake ground motions in a reasonable way. Most of the proposed theories are based on deterministic approaches and deal with displacement responses. A stochastic acceleration response index is treated here as the objective function to be maximized. The power (area of power spectral density function) and the intensity (magnitude of power spectral density function) are fixed and the critical excitation is found under these restrictions. It is shown that the original idea for stationary random inputs can be utilized effectively in the procedure for finding a critical excitation for nonstationary acceleration responses of nonproportionally damped structural systems. Several numerical examples are presented to demonstrate the characteristics of generalized time-varying frequency response functions for models with various stiffness and damping distributions.

This paper presents a nontraditional uncertainty treatment for mechanics problems. Uncertainties are introduced as bounded possible values (intervals). Interval finite-element methods, developed by the authors, are used in the present formulation. To account for different types of uncertainties in linear static problems an interval linear system of equations is developed. A guaranteed enclosure for the solution of interval linear system of equations is achievable and usually is not sharp and very conservative; however, an exact enclosure is not known to be obtained in the general case of such systems. In this work, a very sharp enclosure for the solution set, due to loading, material and geometric uncertainty in solid mechanics problems, is obtained. The new formulation is based on an element-by-element technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Most sources of overestimation were eliminated, and a very sharp solution is obtained. A number of numerical examples are introduced.

A transversely isotropic, viscoplasticity model is formulated as an extension of Bodner's model. Account is made of inelastic deformation that can occur in strongly anisotropic materials under hydrostatic stress. The extended model retains the simplicity of the Bodner model, particularly in the ease with which the material constants are determined. Although the proposed model is based on a scalar state variable, it is capable of representing material anisotropy under the assertion that history-induced anisotropy can be ignored relative to strong initial anisotropy. Physical limitations on the material parameters are identified and discussed. The model is applied to a W/Cu metal matrix composite; characterization is made using off-axis tensile data generated at NASA Glenn Research Center.

Experimental and analytical investigations have shown that sand-lime mortar joints harden in a nonlinear manner after initial yield; then upon reloading, respond in a linear elastic manner under certain conditions of thrust and moment. This paper presents a method to predict this behavior using an exponential hardening model for the sand-lime mortar. Equations are developed to predict: (1) the joint rotation and shortening for three unique stress states; and (2) the moment/thrust yield conditions under which linear elastic responses are possible upon reloading the joint after the mortar hardens. Results show that joint rotation and shortening are influenced greatly by the thrust intensity and eccentricity. Once the material yields, the nonlinear hardening characteristics of the mortar significantly affect the joint's behavior under loading. Plots of moment/thrust hardening surfaces are presented for various loading conditions of the joint. The results are consistent with earlier findings obtained by using a nonlinear finite element model of a sand-lime mortar joint.

Modeling of the drying of porous materials is often approached by assuming that the gas pressure of the vapor-air mixture remains constantly equal to the outer atmospheric pressure. Use of both experimental and theoretical results reveals that such an assumption is inadequate to account for the weight loss observed during the drying of weakly permeable materials. For such materials, the gas pressure cannot remain constant because no significant convective Darcean transport of the gas can actually occur. In contrast, the evaporation coupled with the diffusion of dry air generates a gas overpressure that propagates within the material and works actively toward a uniform vapor molar concentration. As a consequence, the diffusion of vapor becomes rapidly nonactive as a driving force of moisture transport. Paradoxically, the drying of weakly permeable materials is eventually achieved by the transport of moisture in its liquid form and its evaporation at the sample boundary in contact with the surrounding air. The analysis is carried out through a modeling of which the formulation is based upon macroscopic thermodynamic considerations. It involves a dry-air component and a water component, the liquid and the water-vapor phases being addressed separately.

This paper deals with the problem of orienting short metal fibers (12 mm length, aspect ratio 60) in a reactive powder concrete during an extrusion process to manufacture reinforced tubes. By choosing an appropriate geometry for the die it is possible to orient the fibers in an orthoradial direction, which is the most efficient if one wishes to reinforce the tube for an internal pressure loading. This result is obtained with both a theoretical and an experimental approach. In a theoretical framework the authors carried out numerical modeling with a constitutive behavior deduced from the anisotropic suspensions theory. This calculus enabled the authors to design the shape of the die. Tubes have then been extruded and the fibers' orientation has been measured with optical microscopy.

This paper presents a nondestructive, stress wave technique to evaluate the prestress levels in posttensioned seven-wire strands. Seven-wire steel strands are widely used in various types of prestressed concrete structures. In this study, both experimental measurements and theoretical analysis were conducted. A commonly used 12.7 mm (1/2-in.) diameter seven-wire prestressing strand was studied. Tensile forces up to 111.2 kN (25 kips) were applied to the strand. A numerical analysis was conducted by accounting for acoustoelasticity effects and the dispersion of waves to calculate the prestress levels in the strands. This analysis provides a successful description of the behavior of a longitudinal transient wave traveling through a long, prestressed, circular strand. The calculation correlates well with the experimental observation. The results indicate that the time of flight of the stress waves can be related to the tension level in the strand. Change of wave velocities at different stress levels was evaluated and the accuracy of this technique is discussed. This study proposes a technique that can provide an efficient nondestructive measurement of stress retension levels in posttensioned steel strands.

A robust approach for approximately solving reliability-based optimal design problems, for series structural systems, is developed. The approach reformulates the problems by replacing reliability terms with deterministic functions. The reformulated problems can be solved by existing semiinfinite optimization algorithms, producing solutions that are identical to those of the original problems, when the limit-state functions are affine, or when first-order reliability approximations are used. An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, allowing flexibility in the choice of the optimization algorithm and the reliability method. Three sets of examples demonstrate applications of the approach.

In this technical note, we present the bifurcation analysis of a generalized Drucker-Prager formulation. To this end, the elastoplastic localization properties are cast in the form of an elliptical envelope condition in the σ_N − τ_N coordinates of Otto Mohr, whereby, the tangency condition of the localization ellipse and the major principal circle determines the criticality and type of failure mode.

Carbon/epoxy FRP (Fiber Reinforced Plastic) rebars were produced with the pultrusion technique. Concrete beams reinforced with these rebars were subjected to static and cyclic 3-point bending. Flexural cracking is arrested by an adequate bond between the FRP and the concrete because of the use of a carbon fiber overwrap on the otherwise smooth pultruded rods. In spite of the brittle nature of the FRP rods and the concrete, their combined behavior demonstrate ductility in excess of what is typically expected from reinforced concrete. An analytical evaluation of the fracture energy shows that such ductility is due to the large fraction of the total strain energy that is consumed in the formation of distributed cracking in concrete. Therefore, if an adequate bond can be provided, the strain-to-failure of the FRP determines the ductility and failure mode of FRP reinforced beams.

Progressive fiber debonding in steel fiber/cementitious matrix composites has been studied using a single fiber pullout test that permits simultaneous measurements of the load versus crack opening displacement relationship and Moiré interferometry fringe patterns. Analysis of Moiré interferometry patterns allows the fiber axial and interfacial shear stresses to be calculated along the entire fiber length. The interfacial shear stress distribution along the debonded length of the fiber indicates a steep decrease in shear stress with interfacial slip, from 6 to 1 MPa for 7 μm of fiber slip and a crack opening displacement of 22 μm. These results suggest that improvements in the toughness of cement-based composites could be achieved by developing materials in which the decrease in shear stress is less severe.