Journal of Engineering Mechanics

A nonlinear, large deformation beam/column formulation is used to model the behavior of the human spine under compressive load. The stabilizing roles of muscles are accounted for using Patwardhan’s assumption that muscles act to direct the load along the tangent of the column. Three aspects of the spinal structure are then investigated. First, we look at the effects of two different assumptions for the action of muscles, leading to significant differences in the spine behavior. Second, the difference in mechanical properties between the vertebrae and the spinal disks is explored. Third, a nonlinear mechanical response of the spinal disk that arises from a two-step hierarchical homogenization technique is used. It is found that these factors have an important influence on the overall behavior of the spine structure. The present formulation offers a versatile model to investigate various features of the human spine, while remaining affordable computationally. It also provides an interesting framework for future multiscale studies of the human spine.

A beam finite-element formulation following Euler-Bernoulli beam theory is presented for geometrically and materially nonlinear analysis of rectangular concrete-filled steel tube (RCFT) beam-columns. The formulation is geared for conducting transient dynamic analysis of composite steel/concrete frame structures. The element stiffness and internal forces were derived through adopting a mixed finite-element approach based on the Hellinger-Reissner variational principle. The load transfer between the steel and concrete constitutive materials was provided through steel and concrete interface via friction and interlocking. Six extra translational degrees-of-freedom (DOFs) were added to the conventional 12 DOF beam element to quantify the differential displacement between the two media. The formulation was verified for a range of geometrically nonlinear test problems and geometrically and materially nonlinear RCFT experimental test specimens from the literature. Strong correlation and convergence characteristics were achieved compared to the published results.

In performance-based seismic design, general and practical seismic demand models of structures are essential. This paper proposes a general methodology to construct probabilistic demand models for reinforced concrete (RC) highway bridges with one single-column bent. The developed probabilistic models consider the dependence of the seismic demands on the ground motion characteristics and the prevailing uncertainties, including uncertainties in the structural properties, statistical uncertainties, and model errors. Probabilistic models for seismic deformation, shear, and bivariate deformation-shear demands are developed by adding correction terms to deterministic demand models currently used in practice. The correction terms remove the bias and improve the accuracy of the deterministic models, complement the deterministic models with ground motion intensity measures that are critical for determining the seismic demands, and preserve the simplicity of the deterministic models to facilitate the practical application of the proposed probabilistic models. The demand data used for developing the models are obtained from 60 representative configurations of finite-element models of RC bridges with one single-column bent subjected to a large number of representative seismic ground motions. The ground motions include near-field and ordinary records, and the soil amplification due to different soil characteristics is considered. A Bayesian updating approach and an all possible subset model selection are used to assess the unknown model parameters and select the correction terms. Combined with previously developed capacity models, the proposed seismic demand models can be used to estimate the seismic fragility of RC bridges with one single-column bent. Seismic fragility is defined as the conditional probability that the demand quantity of interest attains or exceeds a specified capacity level for given values of the earthquake intensity measures. As an application, the univariate deformation and shear fragilities and the bivariate deformation-shear fragility are assessed for an example bridge.

Finite-element analysis of strain localization based on classical theory of continuum mechanics suffers from pathological mesh dependence when strain softening models are used. For quasistatic problems, the mesh dependence is demonstrated through an analysis of the tangent stiffness matrix of a one-dimensional problem. To regularize the mesh dependence, a nonlocal strain softening model is proposed, which is based on the nonlocal plasticity theory and the representative line element. Both analytical and numerical solutions of strain localization with the proposed model are developed and compared with each other. The model is also applied in the numerical simulation of a direct tensile test of a concrete specimen in the existing literature, and reasonable agreement is achieved between numerical solutions and the experimental response.

A mesoscale three-dimensional finite-element model is set up to model two-dimensional triaxially braided composites. Unit cell scheme is used to take into account braiding architecture as well as mechanical behavior of fiber tows, matrix, and fiber tow interface. A $0°/\pm 60°$ braiding configuration has been studied. A failure criterion and progressive damage evolution model taking into account fiber tow and tow interface has been applied to theoretically predict interlaminar and intralaminar failure mode. Straight-sided specimen testing has been carried out in both axial and transverse direction. Results obtained in the tests as well as finite-element approaches are discussed. This paper also discusses the main feature of the model through an extensive parameter study. Overall, by comparison of experiment and model results, the applicability of the developed model is assessed and the failure process is investigated; furthermore, conducted parameter study enhances the strength of the model, which lies in the correlation of model parameters and identification of damage modes with experimental data on the overall stress strain curves.

The simulation in real time of heterogeneous systems has to guarantee that the time integration of the equations of motion is always successfully completed within an a priori fixed sampling time interval. Therefore, numerical and/or physical substructures as well as numerical solution methods have to be adapted to the needs of real-time simulations. Monolithic stable numerical methods are implicit and cannot be easily used in real-time applications because of their iterative strategies necessary to solve the nonlinear corrector equations. As an alternative, in the present paper, we consider linearly implicit Rosenbrock-based $L$ -stable real-time (LSRT) compatible algorithms with both two-stage and three-stage. Moreover, other linearly implicit structural integrators used nowadays to perform coupled simulations in real time are introduced too. Successively, typical properties of monolithic algorithms are shown when large time steps are employed. The loss of stability and the reduction of accuracy of these algorithms, when applied to coupled systems caused by kinematically closed loops, are analyzed in-depth through a split-inertia substructured system. In this respect, the benefits of the $L$ -stability property are shown. Finally, the performance of the algorithms under investigation appears in a number of more realistic tests considering both nonstiff and stiff substructures.

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions (referred to as limit-state functions) of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces (referred to as limit-state surfaces) in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the first- and second-order reliability method (FORM and SORM), are based on geometric approximations of the limit-state surfaces near the so-called design point(s) (DP). This paper presents a new efficient tool, the multidimensional visualization in the principal planes (MVPP) method, to study the topology of high-dimensional nonlinear limit-state surfaces (LSSs) near their DPs. The MVPP method allows the visualization, in particularly meaningful two-dimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both time-invariant and time-variant (mean out-crossing rate computation) structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS.

The stress modified critical strain (SMCS) criterion provides a local index for the initiation of ductile fracture in metals as a function of plastic strain and stress triaxiality. Previous research has confirmed the SMCS criterion to be an accurate index for fracture initiation in mild steels and demonstrated its application to civil/structural engineering. To facilitate practical implementation of the SMCS criterion, two key aspects of its calibration for steel materials are examined. The first pertains to the sensitivity of the measured SMCS material toughness parameter to the size of the test coupon. New results from 23 tests of cylindrically notched tension (CNT) specimens of various sizes and notch geometries indicate that the toughness parameter is relatively insensitive to calibration specimen size. This finding validates the use of miniature bar specimens to calibrate the SMCS model for thin plate steels and in-service structures, where extraction of larger coupons is impossible. The second aspect involves the development of closed-form expressions to determine directly the SMCS toughness parameter from CNT tests, thus avoiding the need for interpretation of the test data through finite-element simulations. Based on the results of 54 numerical simulations, encompassing a range of material constitutive properties, specimen geometries, and applied deformations, a semiempirical relationship (based in part on Bridgman’s solution for necked tension rods) is proposed to determine the toughness parameter directly from the CNT bar tests.

Considering the coupling between the in-plane and out-of-plane vibration, the stochastic response of an inclined shallow cable with linear viscous dampers subjected to Gaussian white noise excitation is investigated in this paper. Selecting the static deflection shape due to a concentrated force at the dampers location and the first sine term as shape functions, a reduced four-degree-of-freedom system of nonlinear stochastic ordinary differential equations are derived to describe dynamic response of the cable. Since only polynomial-type terms are contained, the fourth-order cumulant-neglect closure together with the C-type Gram-Charlier expansion with a fourth-order closure are applied to obtain statistical moments, power spectral density and probabilistic density function of the cable response, whose availability is verified by Monte Carlo method. Taking a typical cable as an example, the influence of several factors, which include excitation level and direction as well as damper size, on the dynamic response of the cable is extensively investigated. It is found that the sum of mean square in-plane and out-of-plane displacement is primarily independent of the load direction when the excitation level and viscous coefficient of the damper are fixed. Moreover, the peak frequency and half-band width of the spectra of both the in-plane and the out-of-plane displacements are increasing with excitation level when the damper size is constant. It is also observed that, even though the actual optimal damper size is slightly greater than the one obtained by the complex modal theory, the difference of statistical moment of the cable caused by these two damper size is negligible, so the vibration reduction effect provided by the theoretical optimal viscous coefficient is satisfactory.

Rutting, due to permanent deformations of unbound materials, is one of the principal damage modes of low traffic pavements. Flexible pavement design methods remain empirical; they do not take into account the inelastic behavior of pavement materials and do not predict the rutting under cyclic loading. A finite-element program, based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings, has been used to estimate the permanent deformations of unbound granular materials subjected to traffic loading. Based on repeated load triaxial tests, a general procedure has been developed for the determination of the material parameters of the constitutive model. Finally, the results of a finite-element modeling of the long-term behavior of a flexible pavement with the simplified method are presented and compared to the results of a full-scale flexible pavement experiment performed by Laboratoire Central des Ponts et Chaussées. Finally, the calculation of the rut depth evolution with time is carried out.