Journal of Engineering Mechanics

Subspace identification techniques are a popular parametric time-domain method for extracting modal parameters of a structure under ambient condition. These techniques can simultaneously process a large quantity of data and potentially extract the most information from the measurement. Most of the developed subspace identification techniques, however, assume white-noise input, and hence cannot be used for structures under earthquake excitation. In this study, an input–output recursive combined subspace identification technique is proposed for tracking modal parameters of a time-varying structure under nonstationary earthquake excitation. The technique incorporates an orthogonal projection and an instrumental variable approach to eliminate the effect of earthquake input and measurement noise, respectively. A bi-iteration subspace tracker is then applied to extract step by step the structural modal parameters. The proposed technique is validated numerically on a four-degree-of-freedom structure and experimentally on a three-degree-of-freedom building model. Both numerical and experimental results show that the proposed technique can track structural modal parameters under nonstationary earthquake excitation quite well.

Hybrid simulation is a popular experimental technique whereby only part of a system is physically realized and the remainder is modeled in a computer with a set of actuators and sensors to connect the two subsystems. While the methodology is common, it lacks a theoretical structure that ensures users are getting valid simulation results of the entire system. Further, little attention has been paid to distributed mass systems and those that do not have a beam/column like topology. This work examines three basic issues: (1) an abstract geometric scheme is proposed by which one can reason about hybrid simulation systems and their underlying errors; (2) systems with distributed mass are explicitly considered; and (3) the model system utilized in this study has a distinctly nonbeam/column like system, namely, a Kirchhoff-Love plate with a continuous one-dimensional hybrid system interface. It is demonstrated that such systems are generally viable only below the first fundamental frequency of the system. Furthermore, it is shown that there is a tendency to accumulate global errors, relative to the classical solution, at the slightest introduction of any interface matching error but that these errors are mostly insensitive to further increase in mismatch. Finally, it is found that the different substructures of the systems are subject to resonant excitation at their own independent natural frequencies in addition to those of the complete hybrid system.

This paper presents a theoretical and experimental framework for the application of size-effect analysis to microscratch testing as a means to quantify the fracture properties and internal friction of materials at the microscale. The energetic size-effect law (SEL) for microscratch tests is developed for a general monomeric probe shape in terms of an intrinsic size function. The fundamental idea of the proposed approach is to rescale the scratch response to that of the flat punch, a conjecture that allows one to compare the SEL for different probe geometries, and thus solve for the asymptotic fracture toughness and effective process zone length from scratch tests done on homogenous (acetal homopolymer resin and polycarbonate resin) and inhomogeneous materials (mica ceramic and gas shale). As a material of current interest for controlled fracture studies, two samples of gas shale cored from the Marcellus and Eagle Ford formations are tested and analyzed to quantify all material properties that may be derived from the scratch resistance; namely fracture parameters, asymptotic hardness, strength, cohesion, and internal friction.

This paper is concerned with the bending response of nonlocal elastic beams under transverse loads, where the nonlocal elastic model of Eringen, also called the stress gradient model, is used. This model is known to exhibit some paradoxical responses when applied to beams with certain types of boundary conditions. In particular, for clamped-free boundary condition, this nonlocal model is not able to predict scale effects in the presence of concentrated loads, or it leads to an apparent stiffening effect for distributed loads in contrast to other boundary conditions for which softening effect is observed. In the literature, these paradoxes have been resolved by changing the kernel of the nonlocal model or by modifying the standard boundary conditions. In this paper, the paradox is solved from the nonlocal differential model itself via some related discontinuous nonlocal kinematics. It is shown that the kinematics related to the nonlocal constitutive law lead to the use of moment or shear discontinuities. With such a nonlocal differential model coupled with the nonlocal discontinuity requirements, the beam effectively shows a softening response irrespective of the boundary conditions studied, including the clamped-free boundary conditions, and thereby resolves the paradox. The model is also compared to lattice-based solutions where an excellent agreement between the present nonlocal model and the lattice one is obtained. Finally, the stress gradient model is shown to be cast in a stress-based variational framework, which coincides with a Timoshenko-type model where the shear effect is shown to play the nonlocal role.

Efficiency of a Bayesian model updating algorithm is greatly affected by the choice of variance of prediction error models of different data points (evidence) used for model updating. In the context of structural model updating, a sensitivity-based novel approach is proposed in this work to find these variances without increasing the dimensionality of the model updating problem. Well-established relations of modal data sensitivity toward structural parameters are incorporated in the Bayesian framework to evaluate the prediction error variances. A high-rise shear building is considered for numerical illustration of the approach. Markov chain Monte Carlo (MCMC) simulation technique is employed using the Metropolis-Hastings algorithm to simulate the samples from the posterior distribution. Results are presented as a comparison of unknown parameters obtained using the proposed approach and an approach in which all prediction error variances are assumed to be equal. The study shows that the proposed approach is highly efficient in extracting appropriate information from the data, and therefore enhancing the efficiency of Bayesian algorithm. It also illustrates that the damage locations play an important role in the selection of variances of prediction error models. Furthermore, each data point of evidence can be very effective in estimating the model parameters, if the information contained in the data is exploited effectively.

In order to determine the mode-I (opening mode) dynamic fracture toughness of a rock, cracked-straight-through Brazilian disc (CSTBD) specimens with strain gauges glued on the specimen’s surface were diametrically impacted by a split Hopkinson pressure bar. A hybrid experimental-numerical approach was used to determine the dynamic initiation toughness, and it was also used in conjunction with a universal function to obtain the dynamic propagation toughness. Precautions were taken for getting the time history of dynamic stress intensity factors. Numerical accuracy, stability, and convergence to the solution were guaranteed by analyzing beforehand a widely-recognized benchmark dynamic crack problem. Using the numerical technique the result of the conducted trial analysis corresponded almost exactly with the classical result. The dynamic initiation toughness and dynamic propagation toughness of the rock increase with increasing dynamic loading rate and crack propagation speed, respectively, demonstrating the same variation tendencies reported in related literature. The present study shows that the experimental-numerical approach is both simple and effective.

In nonlinear structural dynamics, direct integration algorithms are used to solve the differential equations of motion after they are temporally discretized. Explicit algorithms do not require iterations and thus avoid numerical problems of convergence by making use of certain approximations. Thus, they are appealing for multi-degree-of-freedom (MDOF) nonlinear dynamic problems. In this paper, the study previously conducted by the authors for nonlinear single-degree-of-freedom systems is extended to MDOF ones to investigate the Lyapunov stability of explicit algorithms. For this purpose, a generic-explicit integration algorithm is formulated for generic MDOF nonlinear systems with softening or stiffening behavior governed by nonlinear functions of the restoring forces. This approach transforms the stability analysis of the formulated nonlinear system to investigating the strictly positive realness of its corresponding transfer function matrix. Furthermore, this is equivalent to a problem of convex optimization that can be solved numerically. Using this approach, a sufficient condition that the bounds where the explicit algorithm is stable in the sense of Lyapunov for the MDOF nonlinear system can be obtained. This approach is applied to two commonly used explicit integration algorithms for a bridge structure and also demonstrated by a generic nonlinear multistory shear building.

The nature of the stress tensor for an unsaturated pendular-state granular medium is investigated by following two micromechanical approaches. Firstly, a stress tensor is analytically derived through stress-homogenization of the medium with internal surfaces being explicitly incorporated in addition to the solid, liquid, and gaseous volumes. As such, the derivation identifies a surface stress tensor associated with the liquid–gas interface endowed with distributed surface tension forces. Secondly, numerical simulations of unsaturated conditions are pursued within the discrete element method (DEM) which can only consider resultant point forces, whereas actual internal forces are indeed distributed in nature, e.g., the liquid pressure which acts over the wetted surfaces. Despite this shortcoming, stress descriptions provided by these two fundamentally distinct approaches are found to be equivalent for unsaturated media subjected to mechanical and hydraulic loading in the pendular regime. Moreover, both approaches indicate that the capillary stress, interpreted as the part of the total stress representing the combined effects of the liquid and gas phases and interfaces, is driven by the microstructure and is thus generally nonspherical.

Because the strength of glass is governed by randomly distributed surface flaws that can propagate catastrophically when the applied stress reaches a critical value, the weakest-link-in-the-chain rationale is the universally accepted interpretation of its significant variability. The two-parameter Weibull extreme value distribution is currently the most commonly used model for structural design, although it is recognized that it fails to capture the experimental data within the region of small failure probabilities, associated with the lowest strengths. However, the precise characterization of this left-hand-side tail of the distribution is crucial for structural applications, for which only very low probabilities of failure are accepted. Experiments have provided evidence of the existence of a lower bound for the strength of glass, a finding that, if proved, could revolutionize the approach to the safety of glass structures. Referring to the large-scale experimental program of the Technical Committee 129—Working Group 8 of the European Committee for Standardization (CEN/TC129/WG8), various generalized statistical distributions like Weibull, either prescribing a strength limit or not, are compared in their ability to interpolate the experimental data using the chi-square goodness-of-fit test. Arguments are presented that support the existence of a minimal strength, which can be reduced, but not annihilated, by the inevitable degradation of the glass surface produced by aging and in-service-related damage.

To make significant advances in concrete engineering, it will be necessary to understand the behavior of cementitious materials at the microscale. To achieve this goal, the nature of damage initiation and growth needs to be understood at very small scales. This research program sought to increase that understanding through the collection of microscale data using X-ray computed tomography (CT). The tensile and compression behavior of both ultra-high performance concrete (UHPC) and conventional concrete were investigated as a part of this program. Relationships were identified between mechanical performance parameters, such as stiffness degradation and work of load, and cracking parameters, such as crack volume and crack surface area, that could be quantified mathematically and implemented into future finite element analysis (FEA) models. The results of this research program have the potential to improve the accuracy and resiliency of numerical models and to provide insight to the materials engineering community concerning the optimal use of UHPC.

The prediction of the stress-strain response of granular soils under large numbers of repeated loading cycles requires subtle changes to existing models, although the basic framework of kinematic hardening/bounding surface elastoplasticity can be retained. Extending an existing model, an extra memory surface is introduced to track the stress history of the soil. The memory surface can evolve in size and position according to three rules that can be linked with physical principles of particle fabric and interaction. The memory surface changes in size and position through the experienced plastic volumetric strains, but it always encloses the current stress state and the yield surface; these simple rules permit progressive stiffening of the soil in cyclic loading, the accurate prediction of plastic strain rate accumulation during cyclic loading, and the description of slightly stiffer stress-strain response upon subsequent monotonic reloading. The implementation of the additional modeling features requires the definition of only two new constitutive soil parameters. A parametric analysis is provided to show model predictions for drained and undrained cyclic loading conditions. The model is validated against available tests on Hostun sand performed under drained triaxial cyclic loading conditions with various confining pressures, densities, average stress ratios, and cyclic amplitudes.

In time-dependent reliability analysis, the calculation of the mean outcrossing or upcrossing rate of a stochastic process from a safe domain or barrier level based on the Rice formula continues to present serious challenge to researchers in the field. Furthermore, the derivation of closed-form analytical solutions to the first passage probability for nonstationary processes has not been very successful except for Gaussian process. The intention of this paper is to drive a closed-form solution for the calculation of mean upcrossing rate of a scalar nonstationary lognormal process from a barrier level. The applicability of this new solution is illustrated in a time-dependent reliability analysis of corrosion-induced concrete cracking. It is found that the results of first passage probability calculated from the derived closed-form solution are in very good agreement with those from Monte Carlo simulation and safety index methods. A merit of the derived solution is that it eliminates unrealistic negative values for inherently positive values of physical properties as a normal distribution would otherwise assume. The paper concludes that the derived closed-form solution for lognormal processes can predict the first passage probability with accuracy. Accurate prediction of first passage probability is of significance in preventing failures of engineering structures during their lifetime.

Simply supported wooden beams nailed to deck boards subjected to wind uplift forces are subjected to compressive stresses at their bottom fibers. Because the restraining action provided by decking is at the top fibers, it is unclear to what extent such restraints are effective in controlling lateral torsional buckling as a possible mode of failure under wind uplift. Present design standards do not have provisions for such cases. Thus, the present study aims to quantify the effect of restraints provided by the deck boards on the lateral torsional buckling capacity of twin-beam-deck systems under wind uplift. Toward this goal, a series of analytical and numerical models were formulated. All models capture the continuous rigid lateral restraint and partial twisting restraint provided by the deck boards. The effects of load type and load position were investigated. The bending stiffness of deck boards was observed to have a significant influence on the lateral torsional buckling capacity of twin-beam-deck systems.

Tensile cracks significantly affect the durability of concrete pavements, leading to an increase in the costs of maintenance and rehabilitation. A model is developed that relates thermal, chemical, and hygral evolutions at small scales due to different distress mechanisms to the risk of fracture at the structural scale. The method is based on application of linear elastic fracture mechanics (LEFM) to eigenstresses that develop in infinite- and finite-length beams on an elastic foundation that represents the subgrade. Axial and bending contributions to the energy release rate are determined for a worst-case scenario of an entirely cracked pavement section in functions of material properties, structural dimensions, and eigenstress forces and moments. By way of example, the model is used to study the risk of fracture of concrete pavements due to two different mechanisms: (1) autogeneous shrinkage at early ages of placing the concrete and (2) thermal cycles at the short term and long term after a temperature change. In addition, scaling relationships are developed that provide insight into the improvement of different structural and material properties for minimizing the risk of fracture.

Creep of cementitious materials results from the viscoelastic behavior of the reaction products of cement and water, called hydrates. In the present paper, a single isochoric creep function characterizing well-saturated portland cement hydrates is identified through downscaling of 500 different nonaging creep functions derived from three-minute-long tests on differently young cement pastes with three different initial water-to-cement mass ratios. A two-scale micromechanics representation of cement paste is used for downscaling. At a scale of 700 microns, spherical clinker inclusions are embedded in a continuous hydrate foam matrix. The latter is resolved, at the smaller scale of 20 microns, as a highly disordered arrangement of isotropically oriented hydrate needles, which are interacting with spherical water and air pores. Homogenization of viscoelastic properties is based on the correspondence principle, involving transformation of the time-dependent multiscale problem to the Laplace-Carson space, followed by quasi-elastic upscaling and numerical back-transformation. With water, air, and clinker behaving elastically according to well-accepted published data, the hydrates indeed show one single power-law-type creep behavior with a creep exponent being surprisingly close to those found for the different cement pastes tested. The general validity of the identified hydrate creep properties is further corroborated by using them for predicting the creep performance of a 30-year-old cement paste in a creep test lasting 30 days: the respective model predictions agree very well with results from creep experiments published in the open literature.

Several different data-driven strategies for nonlinear identification are applied to experimental data exhibiting various types of hysteretic behavior. The experimental data contain displacement and restoring force information for several tests conducted using different configurations of a rheological testing device with various assemblies of nickel titanium-Naval Ordnance Laboratory (NiTiNOL) and steel wire strands. Among the different configurations, the response of the wire strands shows three distinct forms of nonlinear behavior: classical quasi-linear softening hysteresis; strongly pinched, hardening hysteresis; and slightly pinched, hardening hysteresis. The data-driven methods applied for nonlinear identification include polynomial basis functions and neural networks. The polynomial basis nonlinear identification methods are used for the construction and characterization of reduced-order models to gain insight into the physical modeling of the hysteretic phenomena. The neural network methods are found to be more useful for predictive purposes, demonstrating an ability to produce accurate results on both training and testing data.

The equilibrium governing equations of nonlocal anisotropic thin-walled circular cylindrical shell under combined axial compressive force, torsional load, and external pressure are explicitly derived. This is accomplished by appropriately combining the equilibrium equations and the strain-displacement relations according to Flügge’s shell theory and the stress-stain equations of Eringen’s nonlocal elasticity theory. An analytical solution for the buckling of the shells is presented by using the complex method. This model is validated by a good agreement between the results given by the present model and available data in the literature. Furthermore, the model is utilized to elucidate the buckling properties for different load combinations.