Journal of Engineering Mechanics

A constitutive relationship for high-strength concrete (6 to 15 ksi) is developed based on the continuum damage mechanics. The bounding surface concept was employed in the formulations of the theoretical model. A comprehensive experimental program was undertaken in order to establish a database for high-strength concrete under triaxial compression. The stress-strain response of high-strength concrete subjected to triaxial compression was acquired through laboratory experiments. The testing program included three strength categories—6, 10, and 15 ksi (42, 70, and 105 MPa) concretes. The confining pressures (σ₁) employed in the experiments ranged from 1.2 to 12 ksi (8.3–82 MPa). A series of uniaxial tension and compression tests were performed in order to develop the necessary data for the establishment of the failure criterion. Comparison of the stress-strain results indicated good agreement between the theoretical model and the experimental data.

A computational method is proposed for simulating rheological phenomena of a body composed of a material such as soft soil, powder, and granular material under large excitations. These phenomena are considered to be elastic-viscoplastic (E-VP) flows with moving boundaries. Fundamental equations for the dynamics are constructed from the Eulerian viewpoint. The constitutive laws for pressure volume and deviatoric stress strain are E-VP and are expressed by differential equations. The pressure and deviatoric stress are combined to satisfy yield conditions. The equations construct the first-order partial differential equation system. A domain containing an E-VP body is divided into cells by applying a finite difference method to the partial differential equation system. The locations of markers distributed in the body are calculated to trace the moving free boundaries. The collapse of an E-VP square body is shown as an application example.

A powerful and efficient method is presented for finding exact out-of-plane natural frequencies of plane structures composed of curved Timoshenko beams. Initially, exact dynamic stiffnesses are derived from the governing differential equations of motion in a form that can be used directly in the stiffness method of analysis. This enables any appropriate structure to be modeled according to standard techniques, which, in this case, yield a transcendental eigenvalue problem. Then it is shown how any desired natural frequency may be obtained with certainty by employing a modification to a well-established algorithm, which ensures that no natural frequencies can be missed and avoids the usual approximations associated with traditional finite elements. Finally, comparisons are made with published results and an example shows how the natural frequencies of a continuous curved beam are altered when the effects of shear deflection and rotary inertia are considered.

The spectral formulation of the stochastic finite-element method is applied to the problem of heat conduction in a random medium. Specifically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random fluctuations. Using the spectral stochastic finite-element method, this paper analyzes the sensitivity of heat conduction problems to probabilistic models of random data. In particular, both the thermal conductivity and the heat capacity of the medium are assumed to be uncertain. The implementation of the method is demonstrated for both Gaussian and lognormal material properties, modeled either as random variables or random processes.

The effect of joint geometry parameters (joint orientation, joint density, and joint size) and joint transmissivity on the hydraulic properties of jointed rock blocks was examined in two dimensions using joint networks with two joint sets through numerical experiments. The chance for equivalent continuum hydraulic behavior and the average block permeability of jointed rock were found to be very sensitive to the relative orientation of the joint sets in a joint network system. Although both the equivalent continuum behavior and the average block permeability seem to be little affected by the change of the standard deviation of the joint orientation distribution, the degree of permeability anisotropy seems to depend on the standard deviation of the joint orientation especially for anisotropic joint systems. Chance for the equivalent continuum behavior and the average block permeability were found to increase with the increase of joint density and joint size. The chance for equivalent continuum behavior and the permeability anisotropy were found to depend on the distribution of joint hydraulic conductivity. The influence of the joint hydraulic conductivity is more prominent for joint systems with high joint density and large joint sizes. The greater the variation of the hydraulic conductivity value among the joints in a joint set, the lesser the chance for the medium to behave like an equivalent continuum porous medium.

The fracture tensor is a combined measure of joint geometry parameters. The possible relations between the properties of the fracture tensor and the hydraulic properties of jointed rock including the equivalent continuum behavior are investigated in this paper through numerical experiments performed at the two-dimensional level incorporating joint networks with two joint sets. The possibility of a nonzero average block permeability and the equivalent continuum behavior of a joint system can be expressed with the help of the first invariant of fracture tensor (F₀). A threshold value of F₀ (to achieve nonzero block permeability) between 3 and 6 and a cutoff value of F₀ (to achieve equivalent continuum behavior) between 10 and 30 were obtained for the joint geometry configurations studied in the investigation. Both the threshold value and the cutoff value of F₀ were found to depend on the relative orientation of joint sets. Joint systems with low relative orientation angles (for systems with only two joint sets) and low densities do not show hydraulically equivalent continuum behavior. A nonlinear relation seems to exist between the directional permeability and the fracture tensor component for the connected joint configuration when rock blocks contain only minor discontinuities. For rock blocks containing major discontinuities, this relation becomes linear.

One of the open questions is the performance of rate-independent versus rate-dependent constitutive formulations when failure is evaluated at the material and the finite-element levels. In the case of rate-independent descriptions, the underlying tangential material operator exhibits singularities and material branching at limit points of the response regime. In addition discontinuous bifurcation can take place in the form of localization concomitant with the formation of spatial discontinuities. In contrast, rate-dependent descriptions resort to an instantaneous elastic stiffness operator that remains normally positive definite, while degradation is introduced through the time history of inelastic eigenstrains. In fact when the inelastic process does not contribute to the instantaneous material operator one speaks of elastic-inelastic decoupling. As a consequence viscoplastic material descriptions are often advocated to retrofit loss of stability, loss of uniqueness, and loss of ellipticity of rate-independent, inviscid material descriptions. In this paper the failure predictions of viscoplastic Duvaut-Lions and viscoplastic Perzyna material formulations are analyzed and compared with the inviscid elastoplastic formulation. Our attention will be focused on the loss of material stability and on discontinuous bifurcation in the form of localization. The results on the material and on the finite-element level indicate that Duvaut-Lions regularization fails in the limit, when we consider viscoplastic processes with relaxation times approaching zero. In this case, there exists an algorithmic tangent operator for the Newton-Raphson solution of implicit time integration procedures that exhibits loss of stability, loss of uniqueness, and loss of ellipticity in the form of discontinuous bifurcation similar to rate-independent elastoplasticity. On the other hand, localization at the material level indicates that Perzyna viscoplasticity does suppress localization for the entire range of viscosities and thus provides stronger regularization than the Duvaut-Lions viscoplastic overstress model at the cost of excessive degradation when the viscosity approaches zero. These theoretical observations are confirmed with computational simulations of dynamic failure of a flexural member.

A two-dimensional rectangular tank with rigid walls is used as the example for presenting the concepts of fully nonlinear and complete dimensional analysis. The container is subjected to simultaneous action of horizontal and vertical ground accelerations. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The Euler equations as well as the nonlinear, kinematic free-surface boundary condition are used in the analysis. A time-independent finite difference method is used to evaluate the velocity fields and the surface profile of the sloshing fluid. The significance of the nonlinear effect on hydrodynamic force on tank face is studied. The comparison of numerical results evaluated by the complete two-dimensional analysis and the linear superposition (invalid when high nonlinearity is presented) of results evaluated by separated ground exciting is made. Details of the characteristics of nonlinear sloshing as well as of the beating phenomena are described. The occurrence of resonance is also studied.

In the second-order reliability method the principal curvatures, which are defined as the eigenvalues of rotational transformed Hessian matrix, are used to construct a paraboloid approximation of the limit state surface and compute a second-order estimate of the failure probability. In this paper, the accuracy of the previous formulas of SORM are examined for a large range of not only curvatures but also number of random variables and first-order reliability indices. For easy practical application of SORM in engineering, a simple approximation of SORM is suggested and an empirical second-order reliability index is proposed. By the new approximations, SORM can be easily applied without rotational transformation and eigenvalue analysis of Hessian matrixes. The empirical reliability index proposed in this paper is shown to be simple and accurate among the existing SORM formulas with closed forms. The proposed empirical reliability index gives good approximations of exact results for a large range of curvature radii, the number of random variables, and the first-order reliability indices.

In the second-order reliability method, the Hessian matrix is used to construct a paraboloid approximation of the limit state surface and compute a second-order estimate of the failure probability. In this paper, a practical point-fitting second-order reliability approximation is proposed, by which the explicit second-order approximation of the performance function is obtained directly in standard normal space with neither the computation of Hessian matrix nor the computation of gradients of the function. Once the point-fitted performance function is obtained, the failure probability is estimated by the empirical second-order reliability index, which is generally simple and works well compared to other second-order reliability method formulas. For accurate computation of the failure probability, an IFFT method is proposed, from which the failure probability is obtained conveniently using the Inverse Fast Fourier Transformation. The proposed methods are investigated and their accuracy and efficiency are demonstrated using numerical examples.

Two main computational methods have been used in recent years to model the behavior of particulate solids in silos. These are the finite element method and the discrete element method. To assess the current state of the art in the two methods applied to silo problems, and to evaluate their capabilities without bias, an international collaborative project was set up to compare predictions of several silo phenomena. The first of these computational challenges was deemed the simplest: that of filling a silo or container with particulate solid. This paper presents an overview of the findings of this first problem, based on a total of 38 independent calculations. Here the collaborative project is briefly outlined and some deduced outcomes from calculations by continuum analysts are compared. The results of discrete element calculations are described in a companion paper, which also compares the two methods and comments on their strengths and weaknesses.

During the last two decades, many attempts have been made to develop computational models to represent the behavior of particulate solids in silos. Two methods have been used most commonly: the finite element method and the discrete element method. In an attempt to compare the state of the art in the two methods and to make an unbiased assessment of their capabilities, this project has harnessed expertise from all over the world to compare predictions of a group of standardized problems concerning silos. The first of these problems was deemed the simplest: that of filling a silo or container with solid. The challenge was to determine the stress state in the solid and the resulting wall pressures. The problem description and continuum analysis results were presented and discussed in a companion paper. This paper summarizes the discrete element predictions. A comparison is also made between the discrete and continuum analyses. Finally, comments are made on the outcome of the project.

This research uses laser ultrasonic techniques to develop transfer functions that remove the effect of geometric features on experimentally measured Rayleigh waves. These transfer functions are developed using a repeatable, broadband optical source and a high-fidelity sensor, a dual probe, laser interferometer. The transfer functions are developed by comparing the frequency changes between incident and transmitted Rayleigh waves that interact with a prescribed corner. These transfer functions are used to operate on different signals (waves) that contain the effect of both the corner and a defect, to remove the effect of the corner and isolate the contribution of the defect. The accuracy of these transfer functions is demonstrated and the robustness of the proposed technique is established.

Due to the fact that certain brittle extensions of cracks in anisotropic materials are caused by the surpassing of the limit strain by the actual strain produced by the load, a strain criterion (r_e-criterion) is proposed in this paper. Parameter studies of the r_e-criterion for the extension direction and initiating load are carried out. Comparisons between the r_e-criterion, some stress criteria, and the independent experimental results are made. It is shown that the r_e-criterion can predict quite accurately both the extension direction and the initiating load. The r_e-criterion is more general than the stress factor ratio criterion in that it takes into account the influence of Poisson's ratio in predicting the crack extension direction and the initiating load. The r_e-criterion can be reduced to the stress factor ratio criterion in certain cases. The prediction of crack extension direction and initiating load can be quite different using different criteria.