Journal of Engineering Mechanics

This study investigated the time-dependent crack propagation of the rock–concrete interface under sustained loading. First, sustained loading tests were performed on the composite rock–concrete beams under three-point bending with respect to three interface roughness degrees, i.e., natural, $4\times 4$, and $7\times 7$ interfaces, and three sustained load levels, i.e., 80% of the maximum load, the initial cracking load, and 97% of the maximum load. Then, by employing the Norton-Bailey model and the time-dependent fictitious crack model, the constitutive relationships of bilateral materials and the rock–concrete interface were established and the mechanical responses of the rock–concrete interface under sustained loading were simulated. In addition, a crack propagation criterion proposed in this study was applied in the numerical procedure to simulate the time-dependent crack propagation process under sustained loading. The criterion implied that the interface crack propagated when the difference between the average elastic strain energy densities near the crack tip caused by the external load and cohesive stress exceeded that at the initial fracture status under quasi-static loading. The results indicated that the crack propagation under sustained loading could be interpreted from the view of energy balance between the driving energy from the external load and the resistance energy from the cohesive stress. The time-dependent crack propagation under sustained loading experienced three stages, i.e., decelerated propagation, uniform propagation, and accelerated propagation. A linear relationship between the logarithms of the crack mouth opening rate in the uniform propagation period and the failure time was established to predict the failure time of the rock–concrete interface under sustained loading.

The flexural band gaps in a double-beam system on elastic foundations periodically interconnected by local resonators with two degrees of freedom were investigated using the plane wave expansion method. The transmission property of the finite periodic system was examined by the finite-element method to verify the existence of the band gaps. The mechanism of band gap formation was further studied according to the eigenmodes at the edges of band gaps and the transverse deformation patterns. The technique of broadening the band gaps was also proposed. The results indicated that significant attenuation still appears outside the band gaps for the heterolateral transmission due to the counteraction of the approximate symmetric and antisymmetric flexural bands. The band gaps can be effectively broadened, and the propagating waves are even completely eliminated in the last pass band by only adding a spring. It was also observed that increasing the distance between the left and right attached points and the gravity of the resonator gradually from the asymmetric distribution to the symmetric distribution makes two band gaps coupled to form a superwide gap. The presented results emphasize the promising potential of the double-beam system in controlling the propagation of the flexural wave.

In this paper, an element-based deep learning approach named DeepFEM for solving nonlinear partial differential equations (PDEs) in solid mechanics is developed to reduce the number of sampling points required for training the deep neural network. Shape functions are introduced into deep learning to approximate the displacement field within the element. A general scheme for training the deep neural network based on derivatives computed from the shape functions is proposed. For the sake of demonstrations, the nonlinear vibration, nonlinear bending, and cohesive fracture problems are solved, and the results are compared with those from the existing methods to evaluate the performance of the present method. The results demonstrate that DeepFEM can effectively approximate the solution of the nonlinear mechanics problems with high accuracy, while the shape functions can significantly improve the computational efficiency. Moreover, with the trained DeepFEM model, the solutions of nonlinear problems with different geometric or material properties can be obtained instantly without retraining. Finally, the proposed DeepFEM is employed in the identification of material parameters of composite plate. The results show that the longitudinal and transverse elastic moduli of the ply in the composite plates can be accurately predicted based on the nonlinear mechanical response of plates.

Granular materials subjected to compressive cyclic loading of constant amplitude when modeled using an isotropic hardening, elastoplastic Drucker-Prager (DP) model do not accumulate significant plastic strain beyond the first loading cycle. This can lead to predictions of permanent deformations in airfield asphalt pavements that do not compare well with experimental observations. Accordingly, this paper proposes a modification to the existing DP model as a means of accounting for this shortcoming. A new parameter, $\gamma$, is introduced, which causes the yield surface to progressively evolve and shrink in size during successive load cycles to account for microphysical restructuring of the granular material during constant amplitude cyclic loading. The constitutive model is implemented within the finite element code ABAQUS through the user material subroutine UMAT. The model is subsequently tested via 2D finite element analysis on pavement sections by applying it to the granular base and modeling all other layers as linear elastic. Validation is undertaken by comparing rutting with field experimental values from an accelerated pavement testing program. Increased equivalent plastic strain and vertical plastic strains are observed with this modification, thereby resulting in rutting values that are significantly closer to the experimental data than those obtained with the classical DP model.

The fractional-order derivative Zener (FDZ) model can reasonably predict the frequency dependence behavior of rubber-like materials. However, its capability to capture nonlinear behaviors is limited. In our previous work, we built a horizontal shear model of a multidimensional rubber-like base isolation bearing, modifying the FDZ model to compensate for its inability to reproduce the nonlinear behaviors of amplitude dependence and slow stabilization. In this paper, the tension-compression behavior of the same bearing in the vertical direction is studied, where strain-stiffening nonlinear behavior is exhibited. A different strategy is used to establishing the modified tension-compression FDZ (CFDZ) model, which is shown to have good agreement with experimental results. State-space representation of the CFDZ model is presented and included in modelling a train-bridge-bearing system for dynamic analysis. Simulation results demonstrate that the proposed bearing achieves a high base isolation performance in the vertical direction.

Arches are important components in nanostructures and systems. Because of the remarkable strength of nanomaterials, nanoarches are slender, thus enhancing their vulnerability to geometric instability, such as buckling. Although molecular simulations are often employed to analyze nanostructures, their use in routine analysis/design is formidable due to prohibitively exhaustive computation. Equivalent continuum models were developed as alternatives. The buckling and postcritical phenomena of the classical arch also form an important benchmark problem in nonlinear mechanics. This study investigates the buckling and the postcritical behavior of nanoarch subjected to inward pressure using nonlocal (NL), strain gradient (SG) continuum theory. The governing equations are derived in the form of a sixth-order nonlinear integrodifferential equation, unlike the fourth-order for a classical arch. The equation is then solved numerically using a differential quadrature (DQ) with appropriate boundary conditions. An incremental-iterative arc-length continuation is employed for the solution of the resulting algebraic system of equations. The equilibrium paths are traced for the possible instability modes, such as symmetric/antisymmetric bifurcations, snap-through and limit point instability, ascertained with the internal-external force diagrams. A particular instability mode is triggered at a certain threshold/range of the slenderness ratio of the arch, which is significantly influenced by the NL and SG interactions. These interactions not only cause quantitative changes in the instability behavior but also lead to qualitative changes, such as cessation, shift, and conversion of modes, more prominently for SG arches. Similar to classical arches, the prebuckling nonlinearity is shown to be significant.

A new design of functionally graded graphene-reinforced composite laminated (FG-GRCL) toroidal shell segments in the thermal environment with a piezoelectric layer attached to the surface of the shells is presented in this paper. The piezoelectric FG-GRCL toroidal shell segments are reinforced by a FG-GRCL stringer and/or ring stiffener system. The nonlinear electro-thermo-torsional buckling and postbuckling of the shells are analyzed considering the geometrical nonlinearities described by von Kármán in the framework of the classical Donnell thin shell theory. Airy’s stress function and Galerkin’s process are applied, in which the deflection solution of the shell is approximately presented. The effects of thermal load, volume fraction and distribution type of graphene, piezoelectric layer, geometric parameters of the toroidal shell segments, and stiffeners on the torsional buckling load and postbuckling curves are analyzed and investigated in the numerical investigations.

Hygro-thermal and hydration behaviors exist in concretes at early ages, which inevitably affect their mechanical properties. Accompanying water consumption in the concrete, there are several irreversible thermodynamic processes, including hydration heat production and strength growth. By considering coupled deformation, heat conduction, and a hydration reaction, a thermodynamically consistent continuum theory is developed for concrete at early age. At first, to satisfy the dissipation inequality, the energy dissipation caused by these irreversible processes can be tentatively described by introducing a hydration extent $\ell$, so that a hydration kinetic equation considering the temperature and stress effects is established by linking the reaction rate with the concentrations of reactants. Compared to the Arrhenius linear relation between the reaction rate and chemical affinity, this nonlinear hydration kinetic equation is applicable to complex hydration reactions. Then, a fully coupled nonlinear constitutive model is constructed to interpret the thermo-chemical-mechanical interactions, whose numerical implementation is generated in commercial software ABAQUS using UEL (user-defined element) subroutines. Particularly, the model is used to predict the evolution of elastic modulus and temperature of two kinds of concretes under adiabatic testing: ordinary concrete (OC) and high performance concrete (HPC), which shows good agreement with experimental results. Furthermore, some examples are numerically studied to illustrate the interactions among mechanical deformation, hydration reaction, and heat conduction in concrete at early ages.

Fiber-reinforced soil is a multiphase and multiscale geomaterial and its strength is determined by the properties of the heterogeneous substances of soil and fibers and their coupling interaction mechanical responses. Based on the physical effects such as cohesion and friction generated by the interactions between soil particles and fibers, a fiber-soil cell element was constructed to investigate the influence of fiber characteristics on the shear strength of fiber-reinforced soil. This cell element is capable of describing the internal material information and fiber characteristics of fiber-reinforced soil. Moreover, according to the compatible geometry deformation between the fiber and soil at the microscale, the notion of strain gradient was introduced, and a multiscale and hierarchical fiber-soil cell element model was proposed. Furthermore, a series of unconfined compression tests are conducted to investigate the strengthening effect of fibers on soil, and the theoretical parameters of the proposed model are quantitatively investigated. Results show that the yield stress of fiber-reinforced soil increases with an increase in the length and content of the fiber. The yield stress of fiber-reinforced soil predicted by the proposed fiber-soil cell element model is in good agreement with that of the test result. The research results are significant for the development of a mechanism-based theoretical framework that links different coupling scales.

This paper extends Eshelby’s problem of one inhomogeneity embedded in a homogeneous infinite domain to a bimaterial infinite domain. The equivalent inclusion method (EIM) was used to simulate the inhomogeneity of an inclusion with a polynomial eigenstrain. The fundamental solution of a point force in a bimaterial was used to formulate the domain integral over the inclusion. For a finite bimaterial domain, the boundary integral equation (BIE) takes into account the boundary responses by a single domain instead of utilizing the conventional multiregion BIE scheme. The EIM can be used similarly, and the elastic field can be obtained with tailorable accuracy based on the order of the polynomial eigenstrain. The algorithm is particularly suitable to simulate a defect in thin film–substrate systems or other similar bilayered materials. The stress concentration of a microvoid embedded in a bilayered solar panel was investigated. The size and location of the void relative to the interface exhibited considerable effects on the stress concentration factor. Numerical case studies demonstrated the effectiveness and accuracy of the algorithm, and parametric studies showed the boundary effects on the stress concentration of a microvoid in a finite bimaterial under a uniform far-field strain.

From theory, calibration and application of the equipartition theorem of statistical physics to structural failure and instability analysis, we introduce the kinetic temperature of structures as an order parameter to ascertain equilibrium and out-of-equilibrium states in structural mechanics. Set within the framework of molecular dynamics-based structural mechanics, this is achieved by connecting the set of momentum balance equations to an outside bath reservoir maintained at a reference temperature history through the Nosé-Hoover thermostat. The problem thus comes down to solving the momentum balance equation with a dissipative mass damping term, which evolves in function of the difference in temperature between the structure’s kinetic temperature/energy and the bath temperature. Following the Zeroth Law of Thermodynamics, it is recognized that a structure is in (thermal) equilibrium as long as the structure’s kinetic temperature attains the bath temperature; whereas it is out-of-equilibrium when the open system (structure plus bath) exhibits a sustained temperature difference. In this case, the structure has exhausted its fluctuation-dissipation capacity, which is indicative—for structures—of a progressive failure and instability. The implementation of the kinetic temperature as an order parameter in structural failure and instability analysis is illustrated for a prototype five-storey building subject to excessive wind and fire loads. It is suggested that the proposed order parameter becomes an integral part of the structural engineering toolbox for resilience studies of buildings and structures.

Continuous cables are widespread in various fields, and mechanical analysis is an important issue in their application. The structural responses of frictional continuous cable systems under external loads are related to the load path. The influence of load path has seldom been considered in the existing analysis methods. This paper proposes a novel approach for the mechanical analysis of continuous cable systems considering the influence of load path. The constitutive relation of the frictional continuous cables was derived, in which the sliding amount parameters were eliminated. The computational frameworks for both definite and indefinite load path cases were proposed. For a definite load path, the structural responses can be uniquely determined by successively trials and modifications of the nodal sliding state. For an indefinite load path, a formula of all the possible structural responses was derived, and the ranges of the structural responses can be obtained. All computations in the approach were converted to matrix operations. The effectiveness and practicability of the proposed approach were demonstrated by two typical numerical examples.

This paper considers the anisotropic frost heave that occurs in frozen soils during thawing and investigates the dynamic response of tunnel systems in such regions to a uniformly distributed load. The phase change of ice to water is assumed to cause the layers of frozen and unfrozen soil to move relative to one another. Analytical solutions were obtained for the displacements and stresses of the tunnel lining, layer of frozen soil, frozen surface, and layer of unfrozen soil under loading during thawing. The boundary conditions and continuity conditions of contact surfaces made from different media were used to obtain the unknown parameters. Through parametric analysis, the dynamic response of the tunnel system under various thawing circumstances was determined. The results demonstrated that the thawing of frozen soil surrounding the tunnel lining can reduce the influence of the load at various positions of the soil under different conditions without affecting the structural stability. Many factors affect the dynamic response of cold-region tunnel systems when the surrounding frozen soil starts to thaw and exhibits anisotropic frost heave. The safe construction and operation of tunnel projects under such conditions can be achieved through the adjustment of the medium parameters.

An accurate nonlinear hygrothermal-electro-elastic (HTEE) buckling analysis of piezoelectric fiber-reinforced composite cylindrical shells subjected to the coupled loading effects of axial compression and hydrostatic pressure was established by considering the nonuniform prebuckling effect. Nonlinear governing equations were derived based on higher-order shear deformation theory and Novozhilov’s nonlinear shell theory. Accurate critical buckling stresses and pressures and explicit buckling modes for both axisymmetric and nonaxisymmetric buckling were obtained by the Galerkin method. A comparison between the new prediction and existing results is presented and excellent agreement is reported. A comprehensive parametric study of geometric parameters, end conditions, distribution patterns, and hygrothermal-electric multiphysical fields on the buckling behavior of HTEE composite cylindrical shell is also analyzed and discussed.

Abstract

The mesoscale structure generated in concrete plays a significant role in the mechanical properties and local failure behavior of mesoscale concrete. This work proposes a novel rigid-block discrete-element method (RB-DEM) for concrete modeling with random mesoscale structure. The results of the uniaxial compression using the RB-DEM demonstrated satisfactory agreement with experimental data. The RB-DEM does not only show satisfactory performance in simulation but also it is simple to use. The RB-DEM model can be built from any finite-element mesh generator, either open source codes or commercial software, which are readily available. The interfacial transition zone (ITZ) is modeled directly by assigning the weakened contact model or parameter at the interface between aggregate and mortar. The effects of ITZ parameters, aggregate volume fraction, and geometric shape on the stress–strain curve and crack propagation are discussed. This work provides a novel and efficient tool for the mesoscale fracture simulation of concretelike material considering the relatively large time-step of the DEM.

Practical Applications

Concrete is one of the most common building materials, and its mechanical properties and crack evolution under pressure are extremely important for practical engineering construction. With the development of computer performance, scholars have used software or code to simulate experiments to improve efficiency and save costs (this is known as numerical simulation). This paper proposes a novel method named rigid-block DEM to simulate uniaxial compressive strength test of concrete, and the results were highly similar to the actual experimental results. This method can help researchers further study the influence of various concrete parameters on its performance. Compared with the traditional methods, the rigid-block DEM has abundant advantages such as simple model generation and high calculation efficiency, which provides a valuable reference for the future numerical simulation of concrete, and has certain guiding significance for engineering construction.

The log-law of the wall in the overlap for wall-bounded turbulent flows is rederived from a pure dimensional analysis and functional equation based on three experimental facts: (1) in the inner flow region, the mean velocity distribution is dominated by the viscous length scale; (2) in the outer flow region, the mean velocity distribution is dominated by the largest eddy size or the boundary layer thickness; and (3) there is an overlap between the inner and outer regions. These facts lead to a functional equation that yields a universal log-law in the overlap. Hence, the log-law is independent of any turbulence model, and it is an axiom accepted widely in fluid mechanics.