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In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.

In this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.

The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.

The study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

Polyurethane concrete (PUC), as a new type of steel bridge deck paving material, the bond-slip pattern at the interface with the steel plate is not yet clear. In this study, the mechanical properties of the PUC and steel plate interface under the coupled action of temperature, normal force and tangential force were explored through shear tests and numerical simulations. An analytical model for bond-slip at the PUC/steel plate interface and a predictive model for the shear strength of the PUC/steel plate interface were developed.

The new shear test device designed in this paper overcomes the defect that the traditional oblique shear test cannot test the interface shear performance under the condition of fixed normal force. The universal testing machine (UTM) test machine was used to adjust the test temperature conditions. Combined with the results of the bond-slip test, the finite element simulation of the interface is completed by using the COHENSIVE unit to analyze the local stress distribution characteristics of the interface. The use of variance-based uncertainty analysis guaranteed the validity of the simulation.

The shear strength (τ_f) at the PUC-plate interface was negatively correlated with temperature while it was positively correlated with normal stress. The effect of temperature on the shear properties was more significant than that of normal stress. The slip corresponding to the maximum shear (D₁) positively correlates with both temperature and normal stress. The interfacial shear ductility improves with increasing temperature.

Based on the PUC bond-slip measured curves, the relationship between bond stress and slip at different stages was analyzed, and the bond-slip analytical model at different stages was established; the model was defined by key parameters such as elastic ultimate shear stress τ₀, peak stress τ_f and interface fracture energy G_f.

The solder‐joint reliability of solder‐bumped wafer level chip scale package (WLCSP) on microvia build‐up printed circuit board (PCB) subjected to thermal cycling conditions is investigated in this study. The 62Sn36Pb2Ag solder joints are assumed to be: an elastic material; an elastic‐plastic material; and a creep material which obey the Garofalo‐Arrhenius steady‐state creep constitutive law. The stress and strain in the corner solder joint of the WLCSP assembly are presented and compared for these three material models. Also, the results presented herein will be compared with that from creep analysis of the WLCSP on PCB without microvia build‐up layer.

Granular materials possess multiscale structures, i.e. micro-scales involving atoms and molecules in a solid particle, meso-scales involving individual particles and their correlated structure, and macroscopic assembly. Strong and abundant dissipations are exhibited due to mesoscopic unsteady motion of individual grains, and evolution of underlying structures (e.g. force chains, vortex, etc.), which defines the key differences between granular materials and ordinary objects. The purpose of this paper is to introduce the major studies have been conducted in recent two decades.

The main properties at individual scale are introduced, including the coordination number, pair-correlation function, force and mean stress distribution functions, and the dynamic correlation function. The relationship between meso- and macro-scales is analyzed, such as between contact force and stress, the elastic modulus, and bulk friction in granular flows. At macroscales, conventional engineering models (i.e. elasto-plastic and hypo-plastic ones) are introduced. In particular, the so-called granular hydrodynamics theory, derived from thermodynamics principles, is explained.

On the basis of recent study the authors conducted, the multiscales (both spatial and temporal) in granular materials are first explained, and a multiscale framework is presented for the mechanics of granular materials.

It would provide a paramount view on the multiscale studies of granular materials.

The purpose of this paper is to investigate the effect of anisotropy in terms of a single parameter indicating strengthening or weakening in the tangential direction in composite disc with hyperbolically varying thickness introduced presumably by processing or due to alignment of dispersed reinforcements during flow of the matrix.

Mathematical model to describe steady-state creep behavior in an anisotropic rotating disc made of Al-SiCp composite containing 30 vol% of SiC particles. The creep behavior of the composite has been described by Sherby's law. The creep parameters in the law have been determined using the regression equations developed on the basis of available experimental results in the literature. Stress and strain rate distributions for isotropic disc (a=1) have been compared with those obtained for anisotropic composites with characteristic parameters a=0.7 and 1.3.

The study revealed that the change in the stresses by anisotropy in composite disc is relatively small while anisotropy introduces significant change in the strain rates. It is concluded that the radial strain rate always remained compressive for the isotropic composite as well as the anisotropic disc with a greater than unity (a=1.3). However, it becomes tensile in the middle region of the disc when it is less than unity (a=0.7). If a is reduced from 1.3 to 0.7, the variation of tensile strain rate in the tangential direction remains similar, but the magnitude reduces, i.e. the strength in tangential direction is enhanced.

This study puts forward an analytical framework for the analysis of creep stresses and creep rates in an anisotropic rotating disc with hyperbolically varying thickness.

The purpose of this paper is to obtain an insight into the effects of sliding and/or joint opening at the contraction, perimeter and concrete lift joints on the nonlinear seismic response of arch dams.

The seismic behavior of a typical thin double curvature arch dam is studied by a nonlinear finite element program developed by the authors. Joints are modeled with the use of zero thickness interface elements. Various constitutive relationships are implemented to account for sliding and opening along the joints. Effects of joint sliding parameters and foundation rock flexibility are also considered in the analyses.

The findings provide information about dynamic stress distribution through the dam body and stability of the dam as a whole and also the local stability of the most critical concrete blocks in the dam body.

Useful information for designing new arch dams or seismic evaluation of constructed dams.

This paper takes into account the stability of concrete blocks in the dam body as well as stability of the structure as a whole. Except for contraction joints, perimeter and concrete lift joints are also modeled. Practical as well as detailed models of sliding are provided for the analyses. The paper offers practical help to design and dam engineers.

The purpose of this study is to present a simplified analytical method to estimate ground lateral displacement due to excavation. Excavations of foundation pit will inevitably lead to soil movements that may adversely impact surrounding facilities or structures. Thus, estimation of the ground displacement induced by excavation is essential in engineering practice.

Based on a theory of elastic mechanics, a simplified analytical method for predicting the ground lateral displacement resulting from foundation pit excavation is proposed.

As the distance from the soil to the supporting structure increases, the maximum ground lateral displacement decreases nonlinearly but at a reduced rate. Poisson’s ratio of soil has a mild influence on the ground lateral displacement, whereas the influence of the supporting structure’s deflection modes is significant.

The advantage of the proposed simplified analytical method lies in that it considers the supporting structure’s arbitrary deflections, giving it wider practical applicability than previous methods.

This study sets out to compare the response of three‐dimensional (3D) woven composites subjected to high strain rate (HSR) compression loading with the dynamic response.

The 3D composites were manufactured using Kevlar woven fabrics with epoxy resin system utilising vacuum bag moulding approach. Samples were subjected to HSR compression loading in three directions using a modified split Hopkinson's pressure bar.

Peak stress and stiffness of 3D composites were higher for dynamic loading when compared with static loading in case of both in‐plane direction and out‐of‐plane direction. The peak stress and modulus increased with the increase in strain rate for both in‐plane direction and out‐of‐plane direction. Peak stress and dynamic modulus were higher when the samples were loaded in the fill direction compared with the warp direction loading. The failure strain in through‐the‐thickness direction was far higher than in in‐plane warp and fill direction.

Other strength parameters of 3D composites could be studied.

The study provided the strength comparison of 3D composites in different situations.

The paper provide data on 3D composites for engineering applications.

The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures.

In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF).

In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness.

An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method.

An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

A transient dynamic finite element procedure is presented for failure analysis of centrally‐impacted laminated composite pretwisted rotating plates. A nine‐noded, three‐dimensional degenerated composite shell element is developed and used for the present finite element formulation. Effects of transverse shear deformation and rotary inertia are included. The strength‐of‐material type failure criteria are adopted and the “total ply discount” approach is used as the stiffness reduction model. The dynamic equilibrium equation is derived by applying Lagrange’s equation of motion and the investigation is carried out for moderate rotational speeds for which the Coriolis effect is negligible. The modified Hertzian contact law is utilized to compute the contact force between the impactor and the laminated plate. Impact failure analyses of pretwisted rotating plates are performed to investigate the effects of angle of twist, rotational speed and laminate configuration.