Journal of Engineering Mechanics

A theoretical study of wave modes in a system of layered materials is presented. The system consists of a floating linear viscoelastic layer over inviscid water. The viscoelastic cover is assumed to obey the Voigt constitutive law. As in many other layered systems, multiple wave modes are discovered. Guided by the roots under pure elastic and pure viscous conditions, the nature of all roots in the dispersion relation is identified for the viscoelastic case. Wave modes include the evanescent, gravity, shear, pressure, interfacial, and Rayleigh-Lamb. All of these previously known waves in elastic solid or fluid over fluid systems are found in the present system of a viscoelastic material floating over water. An analytic criterion for the presence of mode swap in cases with low viscosity is obtained, and the origin of this mode swap phenomenon is discussed. In the vicinity of mode swap, both wave modes are important. Away from this region, the gravity wave mode dominates the free-surface motion.

A simple analytical model for calculating the vibration frequencies of anchor span strands in suspension bridges is proposed in this study. The vibration frequencies of strands are important indicators of tension force and critical in construction control. Most existing methodologies either ignore the connecting rods in anchor spans or require a complex finite-element analysis to ensure accurate calculations. A simple model is proposed for rapid and efficient analysis that includes the geometric and material properties of connecting rods. The calculation results of the proposed model are compared with and verified against those of existing solutions in literature and finite-element simulations. Afterward, the proposed method is applied to the Nanxi Yangtze suspension bridge. The effects of the length and material parameters of connecting rods on the calculation of strand tensions are parametrically discussed. Conclusions and recommendations for future strand tension analysis and control are also presented.

Multistable structural members are extensively used in various fields, including microelectromechanical systems (MEMS) actuation, sensing, and energy harvesting. The multistable configuration of elements can be obtained through their elastic postbuckling response. Under quasi-static excitations, the snap-through transitions of buckled elements constitute a useful tool to generate high-rate excitations for piezoelectric transducers. Yet, more efficient energy harvesting and accurate sensing requires that buckling events happen at specific loading levels. This paper investigates the control of snap-through events by using beam assemblies. Multiple bilaterally constrained beams were arranged in parallel and subjected to axial displacement–controlled loading. Experimental studies show that snap-buckling transitions can be controlled by changing the geometry of the assembled beams. An analytical model was developed to investigate the effect of system parameters on its postbuckling response. Results show that transitions are mainly controlled by the beams’ thicknesses and lengths. By tuning both parameters, the system can be designed to snap at a desired axial displacement. In this paper, the assemblies were designed to transition at equally spaced axial displacements. However, other displacement combinations can be achieved.

The classical critical state theory of granular mechanics makes no reference to the anisotropy of the material and has thus raised questions over the uniqueness of the critical state when fabric anisotropy is taken into consideration. The recently developed anisotropic critical state theory (ACST) suggests that at a critical state the fabric anisotropy tensor acquires normwise a unique normalized critical state value, while the orientation depends on the shearing mode. Consequently it follows that for the same granular material under the same loading conditions, the fabric anisotropy tensor at the critical state should be independent of the initial fabric anisotropy. The fabric tensor in the ACST is referred to in a general sense, not specifying what entity it is constituted of. The present study investigates the evolution of three commonly used fabric tensors based on particle orientation, contact normal, and void vectors, under constant mean effective stress biaxial loading using the two-dimensional discrete element method (2D DEM). These fabric measurements provide a relatively comprehensive coverage of the fundamental characteristics of the particle-contact-void system of a granular material. Global shear banding is avoided in the biaxial simulations to keep the samples as homogeneous representative volumes during loading. The analysis confirms the existence of a unique fabric based on each of the three fabric tensor formulations for the same granular material under the same loading conditions at a critical state. The relationship between the void vector fabric tensor and the contact normal and particle orientation fabric tensors is also tentatively explored. Different fabric quantities (including scalars such as the void ratio and fabric tensor norm and orientation) are found to require different levels of deformation to reach their respective critical states.

This paper presents a general formulation for the distortional analysis of beams of arbitrary cross section under arbitrary external loading and general boundary conditions. The nonuniform distortional/warping distributions along the beam length are taken into account by employing independent parameters multiplying suitable deformation modes accounting for in-plane and out-of-plane cross-sectional deformation (distortional/warping functions). The paper proposes a novel procedure for cross-sectional analysis which results in the solution of separate boundary value problems for each resisting mechanism (flexure, torsion) on the cross-sectional domain instead of relying on eigenvalue analysis procedures encountered in the literature. These distortional and warping functions are computed employing a boundary element method (BEM) procedure. Subsequently, sixteen boundary value problems are formulated with respect to displacement and rotation components as well as to independent distortional/warping parameters along the beam length and solved using the analog equation method (AEM), a BEM-based technique. After the establishment of kinematical components, stress components on any arbitrary point of each cross section of the beam can be evaluated, yielding a prediction in good agreement with three-dimensional finite-element method (FEM) solutions, in contrast to conventional beam models.

In this paper, a new structure-dependent unconditionally stable time-integration method is presented for structural dynamic analysis. The proposed method not only benefits from a semiexplicit formulation, but also inherits the advantages of the Bathe composite scheme. In fact, numerical characteristics of the suggested algorithm are the same as those in the Bathe composite scheme, except that the proposed method does not require any time-step subdividing, which is one of the drawbacks of the composite scheme. A comprehensive stability and accuracy analysis, including numerical dissipation and dispersion, is carried out in order to gain insight into the spectral properties of the proposed method. For numerical verification, some problems with large numbers of degrees of freedom and geometrical nonlinearity as well as linear behavior are solved by the developed technique. Results demonstrate suitable capability, efficiency, and validity of the proposed method in comparison to other existing schemes.

An important point of shear banding is that during the rotation of principal stress directions, out-of-axes deformation plays a significant role and leads to noncoaxiality between principal stress and principal plastic-strain-rate directions. Although many research works have dealt with the effect of noncoaxiality under plane-strain loading conditions disregarding the intermediate principal stress, here, the effect of noncoaxility on the onset of strain localization is investigated under true triaxial conditions because both noncoaxiality and intermediate principal stress are important factors in the investigation of shear-band formation. Therefore, a three-dimensional (3D) noncoaxial elastoplastic model is proposed and incorporated in the single hardening constitutive model to capture the stress-strain relationships and predict the onset of strain localization under true triaxial conditions for the studied dense sand. The numerical simulations illustrate that the bifurcation points comply well with the peak of the stress-strain curves observed experimentally in true triaxial tests. No bifurcation point is observed in the hardening regime by numerical simulations or experimental results near the triaxial compression condition.

This paper presents an elastic-viscoplastic (EVP) constitutive model in triaxial space and general stress space for isotropic clays. The EVP model is anchored in bounding surface theory along with the mapping rule and adopts a critical-state soil mechanics framework. It incorporates creep effects, and a nonlinear creep function is used in the model. The EVP deformation of clay is integrated considering a reference surface and loading surface. An image parameter is deduced to establish the image surface. The strain-rate tensor of the model contains an elastic-strain-rate tensor and viscoplastic-strain-rate tensor. The model formulation is capable of accounting for composite as well as single-surface ellipses. Parameters of the model can be extracted from conventional oedometer and triaxial tests. The model performance is validated by capturing the behaviors in creep tests, relaxation tests, strain-rate effect tests, and overconsolidation ratio effect tests on Kaolin clay, Hong Kong Marine Deposit clay, and Fukakusa clay. The model is also implemented in a finite-element (FE) code and used to predict the long-term performance of the Nerang Broadbeach Roadway embankment constructed in Australia. The long-term settlement prediction of this embankment is also compared with that obtained from the modified Cam clay (MCC) model. Pertinent details of the theoretical framework of the proposed EVP model along with its validation, FE implementation, and field application are discussed in this paper.

Excessive internal pressure and high temperature are the key reasons for concrete spalling, and there are complex interactions between these two aspects. In the current research, a theoretical model to predict the pore pressure effect on concrete behavior is developed. The temperature effect on concrete is incorporated to estimate the change of pore pressure. In order to obtain the pore pressure accurately, volumetric deformation and damage-related permeability are considered to predict the pore pressure in concrete for both tension and compression. The concrete mechanical behaviors are simulated considering pore pressure effect. The predictions agree well with the experimental results. The deterioration of concrete at elevated temperatures and after heating is predicted; it shows that spalling behavior can be simulated by the developed model with reasonable accuracy.