Journal of Engineering Mechanics

The method of fundamental solutions for solving three-dimensional potential flow problems with an unbounded domain is developed in this paper. Because the present meshless method is free from treatments of singularities, meshes, and numerical integrations, the computational effort and memory storage required are minimal as compared with other numerical schemes. It is a suitable technique for the potential flow problems in an unbounded domain, because it only requires that the field points be located on the body surface to satisfy the impermeable boundary condition without defining an optimal finite-domain computation. For the flow passing an obstacle, the impermeable boundary condition on the body surface can be dealt with by the linear superposition scheme. With the validations for the uniform flow passing a two-dimensional wing section and some three-dimensional benchmark problems, an application of case study for the flow field in the multiconnected unbounded domain is carried out. From the computational point of view, the present numerical procedure based on the method of fundamental solutions is efficient and simple to implement for multidimensional exterior potential problems when compared with the mesh-dependent schemes. Those mesh-dependent methods require a complex mesh generation procedure and confinement to a bounded computational domain for a multiconnected exterior problem.

The perfectly matched layer (PML) is a highly efficient absorbing boundary used for the numerical modeling of an elastic wave equation on an unbounded domain. In this work, the authors are concerned with a second-order unsplit PML for transient elastodymanic problems in a semi-plane medium with finite-element approximations. First, based on the concept of stretched coordinates, an efficient unsplit PML formulation is proposed without higher derivatives. Then a finite-element time-domain scheme of a second-order PML in a displacement formulation is developed, in which the Galerkin method is used in space discretization and a Newmark-type scheme is employed for time stepping. Inside the absorbing layer, only one auxiliary vector is required. Hence, the scheme is cheap to implement and easily coupled with standard finite-element methods. Finally, the accuracy and efficiency of the present unsplit PML is demonstrated in numerical examples with a finite-element time-domain scheme.

Stress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka spruce wood are emphasized, although some for carbon-epoxy composites are included. While some results are similar to those for isotropy, there are significant consequences due to material orthotropy. Maximum stress and strain concentration factors occur at midplane for thin plates but closer to the external traction-free surfaces for thick plates. These factors decrease as the plate surface is approached and reach lower values unrepresentative of the maximum values. Differences between the midplane and/or maximum and surface stress or strain concentration factors in Sitka spruce, range from 8% if the wood grain is parallel to the vertically applied load to 15% when the grain is perpendicular to the load. These values exceed those typically reported for isotropic materials. Stress and strain concentration factors tend to differ in magnitude from each other. The combination of high local stresses and directional strength dependency of orthotropic materials can be particularly important. That maximum stress and/or strain concentrations in thick plates occur on other than the external plate surfaces where they are most readily measured is technically significant. The $E_{11}/E_{22}$ ratio in Sitka Spruce exceeds that in the carbon composite by 60%. However, when loading parallel to the strong/stiff directions, the plane-stress tensile stress concentration factors of the two materials are comparable to each other.

Shear wave propagation in soil is a physical phenomenon and has been used widely for monitoring and seismic property assessment in geotechnical engineering. Shear wave velocity $V_s$ and small-strain shear modulus $G_0$ are the key parameters in defining material response to various dynamic loadings. To date, the dependencies of $V_s$ and $G_0$ on saturation, especially in high suction range, are still not well understood because of the limited testing methodology and experimental evidence. In this study, the authors present a new laboratory instrumentation of measuring shear wave propagation in different types of unsaturated soils. Low relative humidity and water mist injection environment are used for measuring shear wave velocity under both drying and wetting conditions. Bender element technique was used to measure the shear wave responses. Step function was used as excitation, and determination of a first arrival time was identified and consistently used for all shear wave measurements. Shear wave evolution and the calculated $V_s$ and $G_0$ with varying volumetric water content under zero total stress condition along drying and wetting are presented. The effects of different soil–water regimes on the evolution of $G_0$ are examined. It is found that $V_s$ or $G_0$ depends highly on soil types, saturation, and drying/wetting state. Parameter $V_s$ or $G_0$ is the lowest when a soil is saturated and the highest when it is dry—varying from tens of meters per second for $V_s$ or a few megapascals for $G_0$ at full saturation for all soils to up to $\mathrm{1,800}\mathrm{m}/\mathrm{s}$ of $V_s$ or 2 GPa of $G_0$ in clayey soil at dry state. The variability of $V_s$ or $G_0$ on soil type becomes more pronounced as soil has more clayey materials. It is also identified that hydraulic hysteresis of $V_s$ or $G_0$ is prominent only in the capillary water retention regime for all types of soil.

A stabilized discontinuous Galerkin (DG) formulation is presented for transient small deformation contact problems involving friction with application to the modeling of bolted lap joints. The method is an extension of derivations from the quasi-static context, whereby the numerical flux terms acting at the contact interface are consistently derived using variational multiscale concepts. This transient primal formulation naturally accommodates nonconforming meshes and stratified materials such as geological faults. Also, the numerical flux terms involving the stress field at the contacting interface provide a natural mechanism for embedding friction models. Numerical results for nonsmooth transient problems confirm that the DG interface approach does not introduce artificial features into the physical response.

Even at first loading, restrained shrinkage of concrete might significantly affect cracking resistance and short-term deformations. Correct assessment of this effect is of vital importance in constitutive analysis. Recently the authors proposed a methodology for eliminating the shrinkage effect from short-term moment-curvature and tension stiffening relationships. However, owing to rather complex issues of convergence and numerical integration, this approach was difficult to apply in practice. The present study proposes an improvement making the methodology a transparent and mechanically sound tool for analysis. The key strategy for the modification was to reduce a large number of concrete layers to two layers, one tensile and one compressive, the latter being assumed to be linear elastic. The study introduces a new concept of tension stiffening, the hybrid model, combining features of the reinforcement-related and the concrete-related approaches. Like the reinforcement-related approach, it assumes that tension stiffening stresses act in the same area in which tensile reinforcement occurs. To account for the shrinkage effect, tension stiffening is related to the concrete—a material capable of shrinking.

This paper presents a new approach to model the creep behavior of cement paste at early ages. The creep behavior is simulated by applying a time-varying generalized Maxwell model on the individual elements of a finite-element mesh of a simulated three-dimensional microstructure and compared with results in the literature. All mechanical properties of the constituent phases are taken from literature and Maxwell chain parameters are obtained by fitting the intrinsic creep of calcium silicate hydrate (C-S-H). A reasonable agreement between the simulations and the experimental results are obtained by assuming a constant C-S-H density of $2.0\mathrm{g}/{\mathrm{cm}}^3$. It was found that better agreements could be obtained at low degree of hydrations, by assuming a loosely packed C-S-H growing in the microstructure. It was also found that the short-term creep characteristics of C-S-H from nanoindentation can be used to reproduce macroscopic creep at least over a few days. The results show how numerical models can be used to upscale phase characteristics to macroscopic properties of composites.

This manuscript presents a modeling approach based on the extended finite-element method (XFEM) for modeling the mechanical behavior of three-dimensional short fiber composites including interface debonding. Short fibers are incorporated into the XFEM framework as deformable elastic two-dimensional rectangular planar inclusions. Enrichment functions account for both the presence of axial deformable fibers within the composite domain and the progressive debonding along the fiber matrix interfaces. A modeling strategy is provided that is particularly suitable for failure analysis of composites with high-aspect-ratio inclusions, in which direct numerical analysis is computationally intractable. The performance of the proposed XFEM model is numerically assessed by comparing model predictions to the direct finite-element method.

A clayey soil is an electrically charged porous medium whose behavior is sensitive to the variations in the composition and concentration of pore water. Pronounced physicochemical interaction can occur between the solid particle and the pore water so that the clayey soil shows strong chemomechanical coupling effects and complex mechanical behaviors. If the degree of saturation varies the pore-water composition and concentration can also vary, resulting in intensive physicochemical effects in the soil. In this paper, a conceptual constitutive model for unsaturated soils is proposed to explain the influence of pore-fluid chemistry on the chemomechanical behavior of unsaturated clayey soils. A new intergranular stress which can effectively account for the physicochemical effects including osmosis, capillarity, and adsorption is introduced as the stress-state variable. The formulation of the proposed model can lead to a remarkable unification of the experimental results obtained under complex chemomechanical loading conditions. The proposed model is validated by comparing the theoretical calculations with the experimental results. It is shown that the proposed model is capable of addressing the effect of water content, concentration and species variation on the mechanical behavior of the clayey soil.

This paper investigates the alternative strategy of suppressing ground-induced vibrations with supplemental rotational inertia. The proposed concept employs a rack-pinion-flywheel system where its resisting force is proportional to the relative acceleration between the vibrating mass and the support of the flywheels. This arrangement, known in the mechanical networks literature as the inerter, complements the traditional supplemental damping and stiffness strategies used for the seismic protection of structures. The paper shows that the seismic protection of structures with supplemental rotational inertia has some unique advantages, particularly in suppressing the spectral displacements of long period structures—a function that is not efficiently achieved with large values of supplemental damping. The paper shows that this happens at the expense of transferring appreciable forces at the support of the flywheels and proceeds by examining to what extent the finite stiffness and damping of the support of the flywheels affects the dynamics of the system. The proposed concept may be attractive for the seismic protection of bridges given that the rack-pinion-flywheel system strategy can accommodate large displacements.

A multilevel modeling framework for the failure analyses of structures made of steel-fiber–reinforced concrete (SFRC), which allows researchers to follow the effects of design parameters such as fiber type, distribution, and orientation from the scale of fiber–matrix interaction to the structural behavior, is proposed. The basic ingredient at the level of single fibers is an analytical model for the prediction of the pullout response of straight or hooked-end fibers. For an opening crack in a specific SFRC composite, the fiber bridging effect is computed via the integration of the pullout response of all fibers intercepting the crack, taking anisotropic fiber orientations into consideration. For the finite-element analysis of the failure behavior of SFRC structures, interface solid elements are used to represent cracks. The softening behavior of opening cracks is governed by cohesive tractions and the fiber bridging effect. The use of an implicit/explicit integration scheme enhances the computational robustness considerably. Numerical analyses of selected benchmark problems demonstrate that the model is able to predict the structural response for different fiber cocktails in good agreement with experimental results.

Rapidly changing pore pressures are a major cause of soil instability, especially in the context of large-scale infrastructural collapses and geo-hazards. In this paper, the governing equations that control pore pressure transients in deformable unsaturated soils are studied from an analytical standpoint, with the purpose of connecting the mathematical properties of the field equations to the mechanics of saturation-induced soil instabilities. New criteria are proposed to identify the loss of parabolicity of the differential problem that governs the mass balance of the pore fluids and the temporal dynamics of their pressure evolution. It is shown that the fulfillment of such criteria yields an ill-posed mathematical problem that can be related to singularities of the pore pressure rate, as well as to violations of Lyapunov-like stability principles. It is further demonstrated that these expressions bear resemblance to the conditions of loss of controllability in unsaturated soils, thereby linking the occurrence of diffusive instabilities to the lack of uniqueness and/or existence of the underlying constitutive behavior. On the one hand, these findings point out that suction-dependent soil nonlinearity may promote the ill-posedness of the field equations, thus causing possible lack of robustness of the algorithms used for their numerical solution. On the other hand, they establish a connection between the loss of strength of unsaturated soils subjected to wetting and the temporal patterns of suction evolution, thus offering new tools to interpret catastrophic failures in natural settings and engineered geo-systems.

An analytical framework has been proposed to analyze the effect of random structural irregularity in honeycomb core for natural frequencies of sandwich panels. Closed-form formulas have been developed for the out-of-plane shear moduli of spatially irregular honeycombs following minimum potential energy theorem and minimum complementary energy theorem. Subsequently an analytical approach has been presented for free-vibration analysis of honeycomb core sandwich panels to quantify the effect of such irregularity following a probabilistic paradigm. Representative results have been furnished for natural frequencies corresponding to low vibration modes of a sandwich panel with high length-to-width ratio. The results suggest that spatially random irregularities in honeycomb core have considerable effect on the natural frequencies of sandwich panels.