The damage behavior of lightweight aggregate concrete (LWAC) is different from that of normal concrete and mesoscopic simulation has been an effective method to understand the damage and failure process of LWAC. It is important for the reliability of simulation to determine the mechanical properties of individual constituents for LWAC. A micromechanical model of LWAC was proposed by utilizing the nearest-surface distribution functions, the generalized self-consistent scheme and a two-phase spherical model. The prediction method of elastic properties for lightweight shale ceramsite concrete (LWSCC) and an inverse method of parameter for each phase were also proposed. Based on a damage constitutive and a 3D mesoscale model, the damage process of LWSCC was analyzed. Results show that the elastic modulus of ITZ is about 0.70 times that of the cement. The damage caused by compression occurs earlier, but the damage caused by tension finally leads to the failure of the sample under uniaxial compression. The inversion method of elastic properties and damage evolution equations are available to study the damage process of LWAC.

The vibration analysis of beams with cracks is an important problem in the structural dynamics community. In this study, a general model for the vibration analysis of a cracked beam with general boundary conditions was developed and investigated, emphasizing its vibration and power flow characteristics. The beam crack was introduced via torsional and translational coupling springs, which separated the beam structure into two segments, and the corresponding vibration characteristics were investigated via an energy-based formulation in conjunction with the Lagrangian procedure. A boundary-smoothed Fourier series was employed to construct the beam displacement field to avoid boundary differential discontinuities. Various crack statuses, including their depths or positions can be easily considered by adjusting the stiffness coefficient of the artificial springs. Several examples were presented to validate the effectiveness and accuracy of the proposed model. The modal characteristics and forced response of a cracked beam were predicted and analyzed, respectively, with a detailed depiction of the power flow around the crack. The results indicate that the presence of a crack has an important effect on the modal characteristics of an elastically restrained beam, as well as on the power flow distribution across the beam structure. This study can provide an effective tool for the dynamic analysis and power flow mechanism of beam structures with various cracks and complex boundary conditions.

The interaction of non-Newtonian grease with patterned surfaces was considered as a promising approach to find an effective method for reducing friction and wear in rolling contacts. Longitudinal and transverse patterns can retain the lubricant in the contact area and prevent it from escaping under high loads. In this paper, a model has been developed for grease elastohydrodynamic lubrication of surfaces with different patterns to estimate the lubrication parameters such as lubricant film thickness, pressure distribution, and viscous friction. Then several experimental tests are rolled out for different loads, velocities, and surface patterns. Because the friction model estimates only viscous friction, a correlation is recommended for considering the friction due to asperity interaction. This relation is based on average lubricant film thickness results which are calculated from the model. The calculated friction and experimental results have a good agreement. According to the experimental tests, transverse, longitudinal, and isotropic pattern had a lower friction coefficient, respectively. While the isotropic viscous friction coefficient estimated by the model is lower than others. Higher loads and lower velocities cause a higher friction coefficient in all surface patterns.

The lining incorporating yielding elements has been proved to be the most effective solution for tunneling through severe squeezing ground. Unfortunately, there has not been a well-organized method to transfer its beneficial effects into the practical tunnel design. This study aims to provide an analytical model for predicting the behavior of yielding lining supported tunnel. The internal force analysis of the lining is first carried out to determine the optimal installation positions of the yielding elements. Second, the lining incorporating yielding elements is processed as a simplified shell using the equivalent deformation principle. The equation for calculating the elastic modulus of the simplified shell is presented. The analytical solutions for the tunnel displacement and lining pressure are provided in the viscoelastic Burgers rocks, where the installation delay of the lining and the tunnel face advancement effect are taken into account. The proposed analytical model is applied in the Saint Martin La Porte access adit of Lyon-Torino Base tunnel, where the yielding lining was employed. The analytical result provides a good prediction of the time-dependent tunnel convergences in the Saint Martin La Porte access adit. Finally, a comprehensive parametric investigation is performed, including the influences of installation time of yielding lining, yield stress and length of yielding elements. Some inspiring results for the tunnel design are provided.

The wave propagation in an inhomogeneous half space with a semi-cylindrical surface bump is investigated by the means of complex function method. With the origin of the coordinate system as the center, the density of the medium changes radially. To solve the Helmholtz equation with variable coefficients caused by the inhomogeneous of the medium, a conformal transformation technique based on the theory of complex variable functions is adopted. Then, by adjusting the inhomogeneous parameters and comparing with the published analytical results, the correctness of the method in this paper is verified. Finally, the displacement amplitudes of typical observation points on the surface and inside are given, and the effects of incident wave angle, wave number and inhomogeneous parameters on wave energy distribution are analyzed.

In this study, three-dimensional (3D) braided composites are integrated into the substructure of the energy harvester and a 3D braided piezoelectric composite energy harvester (BPCEH) with good performance is proposed. A theoretical model of the 3D BPCEH under the force–electricity–thermal coupling is established, and the output response, which is affected by excitation frequency, load resistance, external excitation and temperature, is simulated. The results illustrate that the braided elastic layer can greatly enhance the mechanical performance of the 3D BPCEH. With the increase in temperature and braided angle, the inherent frequency of the 3D BPCEH migrates into the low-frequency direction and can make the inherent frequency of the 3D BPCEH closer to environmental frequencies.

In this study, a novel nano-electromechanical system (NEMS) mass nanosensor made from a functionally graded porous (FGP) core bonded with piezo-electro-magnetic (PEM) layers is proposed to reveal the combined effect of FGP and PEM on the sensitivity performance of mass nanosensors. First, a theoretical model for this mass nanosensor attached with single/multiple nanoparticles is established via nonlocal strain gradient plate theory. Herein, the FGP core obeying the power-law and sigmoid-law gradient patterns is taken into account, and the inside porosity is considered as even and uneven distributions. Subsequently, the natural frequency shift (NFS) behavior of this mass nanosensor with different attached nanoparticles is investigated via Galerkin method. Finally, a comprehensive parametric analysis is performed to reveal the influence of inhomogeneity index, porosity distributed pattern and porosity volume fraction of core material, size-dependent parameters, as well as the external electric voltage and magnetic potential on the NFS performance of the NEMS mass nanosensor. The obtained results have illustrated that combining PEM surface and FGP core can present significant improvement on the sensitivity of the NEMS mass nanosensor for detecting nanoparticles. The sandwich design strategy for the mass nanosensor proposed in this work would be highly valuable for designing high-performance mass nanosensor in biomedical and industrial applications.

The significant effect of the closed-detached response on the system is often ignored by traditional vibration control and energy-harvesting devices. In this study, we design a composite vibration energy-harvesting damper by combining the lever-type nonlinear energy sink, the three-spring quasi-zero stiffness structure, and the suspended magneto-electric energy harvester. The analytical as well as the numerical solutions are obtained using the harmonic balance method combined with the arc-length extension method as well as the Runge–Kutta method, respectively. Numerical solutions support analytical solutions. The presence of the closed-detached voltage makes composite system voltage harvesting more efficient. In addition, we investigate the performance of vibration control and energy harvesting by changing the dynamic parameters of the system such as attached mass, stiffness, and fulcrum position. Finally, when compared with the traditional absorber, the proposed absorber shows great improvement either in vibration control or in energy harvesting.

The thermo-mechanical coupling mechanism of graphene fracture under thermal gradients possesses rich applications whereas is hard to study due to its coupled non-equilibrium nature. We employ non-equilibrium molecular dynamics to study the fracture of graphene by applying a fixed strain rate under different thermal gradients by employing different potential fields. It is found that for AIREBO and AIREBO-M, the fracture stresses do not strictly follow the positive correlations with the initial crack length. Strain-hardening effects are observed for “REBO-based” potential models of small initial defects, which is interpreted as blunting effect observed for porous graphene. The temperature gradients are observed to not show clear relations with the fracture stresses and crack propagation dynamics. Quantized fracture mechanics verifies our molecular dynamics calculations. We provide a unique perspective that the transverse bond forces share the loading to account for the nonlinear increase of fracture stress with shorter crack length. Anomalous kinetic energy transportation along crack tips is observed for “REBO-based” potential models, which we attribute to the high interatomic attractions in the potential models. The fractures are honored to be more “brittle-liked” carried out using machine learning interatomic potential (MLIP), yet incapable of simulating post fracture dynamical behaviors. The mechanical responses using MLIP are observed to be not related to temperature gradients. The temperature configuration of equilibration simulation employing the dropout uncertainty neural network potential with a dropout rate of 0.1 is reported to be the most accurate compared with the rest. This work is expected to inspire further investigation of non-equilibrium dynamics in graphene with practical applications in various engineering fields.

Lunar dust significantly impacts spacecraft and spacesuits during lunar exploration. The mechanical properties of lunar dust, including adhesion, contact, and wear, are investigated using new mechanical models proposed herein. First, the main contribution for mechanics of this paper was implementing the conical Johnson, Kendall, and Roberts (JKR) model using the energy method for investigating the normal and tangential mechanical characteristics of lunar dust. Additionally, the mechanical properties of lunar dust, such as adhesion, contact, and wear are proposed considering the adhesion effect using the mechanical model. The validity and accuracy of the conical JKR model were verified by comparing the results with experimental data and existing spherical and cylindrical JKR models. Furthermore, a new wear mechanical model for typical lunar dust is proposed considering the adhesion effect. The wear width and coefficients based on the wear model fit well with the existing experiment; therefore, the proposed model can be used to calculate the wear coefficient. Additionally, it can be used to estimate the contact force using an atomic force microscope (AFM) probe and analyze the adhesion between rough particles. The mechanical properties of lunar dust based on our models can be valuable for the characteristic research of in situ resource development and manned lunar landings.

Morphogenesis is a result of complex biological, chemical, and physical processes in which differential growth in biological systems is a common phenomenon, especially notable in plant organs such as petals and leaves. Mechanisms of these biologic structures have been studied in recent years with a growing focus from the mechanics point of view. However, understanding differential-growth-induced shape formation quantitatively in plant organs remains largely unknown. In this study, we conduct quantitative experimental measurement, theoretical analysis, and sufficient finite element analysis of constrained differential growth of a thin membrane-like structure. By deriving the corresponding strain energy expression of a buckled growing sample, we can calculate the shape function of such membrane structures explicitly. The results of this work demonstrate the effect of growth function, geometry characteristics, and material property. Our research points to potential approaches to novel geometrical design and inspirations on the microscale and the macroscale for items such as soft robotics and flexible electronics.

Wave-particle drag effect (WPDE) induced by the interaction between an elastic wave and the carriers in a piezoelectric semiconductor (PS) structure has already become a current hot issue in the field of acoustoelectric conversion. Most related studies are based on the linearized assumption that carrier concentrations are limited to present very small variations such that the nonlinear drift current term can be ignored at all. In this study, the nonlinear effect between an elastic wave and carriers in a PS rod is discussed in detail. The multi-field coupled nonlinear differential equations are numerically solved by finite element method. It is found that the electric transient disturbances are deviated from the standard harmonic distribution by comparing with the linear solutions. The carriers driven by the alternating electric field are more likely to accumulate at the crest when their drift movement motion is consistent with the propagation direction of the traveling wave. Oppositely, the troughs of the carriers tend to depletion due to the nonnegative property of the carriers. In addition, the nonlinear characteristics of the carriers and the dispersion properties of the coupled wave become stronger with the decreasing doping concentrations. These studies will provide guidance for theoretical analysis of wave propagating in PSs and design of acoustoelectric devices.

This research highlights dynamic displacements of laminated porous micro beams resting on elastic foundation under moving load. In the constituted equation of laminated micro scaled beam, the modified coupled stress theory is used in order to determine the size effect. Each layer is considered as identical and porosity distribution and assumed as uniform. Lagrange technique is applied in achieving governing equations, and Ritz method within algebraic polynomials is used for solution. For dynamic solution steps, Newmark average acceleration method is used within time domain. Influences of porosity coefficients, length scale parameter, foundation parameter, order of laminas, fiber orientation angles on dynamically deflections of laminated micro beam are investigated.

Hydrogels are excellent soft materials that can absorb large amounts of water and have applications ranging from biocompatible sensors to soft robots. Experiments have demonstrated that the equilibrium swelling state of hydrogels strongly depends on their preparation and external conditions, such as the as-prepared water content, cross-linking density, and temperature. However, traditional theories based on Flory’s work have failed to capture these dependence effects. In particular, these theories ignore the existence of solvents in the as-prepared state of hydrogels, making them unable to characterize the sensitivity of the swelling and mechanical behaviors to the as-prepared water content. In this study, we propose a constitutive theory that considers the preparation conditions based on statistical thermodynamics. Our theory can precisely predict the swelling ability of hydrogels under diverse preparation conditions and capture the phase transitions of temperature-sensitive hydrogels. We further derived the governing equations for large deformations and solvent diffusion considering their strong coupling effects. Based on our theory, the inhomogeneous deformation-induced solvent migration and delayed fracture of hydrogels were investigated. From theoretical investigations, we revealed the underlying mechanism of these interesting hydrogel behaviors. The theoretical results were further used to guide the design of diverse intelligent structures that can be applied as soft actuators, flexible robots, and morphing the growth of plants.

Experimental evidences show that friction during rotor/stator rubbing may not always obey the Coulomb friction law, which is predominantly adopted in the studies of these kinds. This work is devoted to unveiling the effects of viscous damping in the friction model on forward and backward full annular rubbing responses in a piecewise smooth rotor/stator rubbing system. The effects induced by the viscous friction, which are exclusively different from those with pure Coulomb friction, may possibly be used as the signatures for identifying the presence/extent of viscous friction in rotor/stator rubbing tests. In this work, the boundaries of both forward and backward full annular rub motions are analytically derived based on the stability and bifurcation theory. Due to the introduction of viscous friction, the rotor/stator system changes from a piecewise smooth continuous system to a Fillipov one. The results show that the viscous friction has little influence on the region of backward full annular rubbing responses but has significant effects on the region of forward full annular rub motion. With the increase of the viscous friction, the parameter region of the forward full annular rub shrinks significantly, and the boundary of Hopf bifurcation changes increasingly from supercritical to subcritical. This leads to more complex behaviors in the global response characteristics in comparison with those of the rotor/stator rubbing system with Coulomb friction, for instance, two new quasiperiodic rubbing responses appear beside the quasiperiodic partial rub bifurcating from the synchronous full annular rub, including a new quasiperiodic full annular rub motion that is different from the traditional full annular rubs mentioned above.

Materials-by-design to develop high performance composite materials is often computational intractable due to the tremendous design space. Here, a deep operator network (DeepONet) is presented to bridge the gap between the material design space and mechanical behaviors. The mechanical response such as stress or strain can be predicted directly from material makeup efficiently, and a good accuracy is observed on unseen data even with a small amount of training data. Furthermore, the proposed approach can predict mechanical response of complex materials regardless of geometry, constitutive relations, and boundary conditions. Combined with optimization algorithms, the network offers an efficient tool to solve inverse design problems of composite materials.

In this study, an analysis of nonlinear stability and vibration of functionally graded (FG) variable thickness toroidal shell segments (TSSs) reinforced with spiral stiffeners exposed to axial loading is presented using a combination of semi-analytical and analytical methods. Three types of variable thickness TSSs, including concave, convex, and cylindrical shells (CSs), are studied. Moreover, these structures are reinforced by external spiral stiffeners with various angles whose material properties are considered to be continuously graded along the thickness direction. In this regard, the smeared stiffeners technique is utilized to model the stiffeners, and the Donnell shell theory and the von Kármán equation are applied to derive the nonlinear governing equation for variable thickness TSSs reinforced with spiral stiffeners. Galerkin’s method is then used to obtain a discretized nonlinear governing equation to analyze the shells’ behavior. Also, the fourth-order P-T method is applied to analyze the nonlinear dynamic behaviors and the Budiansky–Roth criteria are used to examine the dynamic post-buckling (DPB) behavior. In this regard, it is noted that in terms of reliability and accuracy, the fourth-order P-T method has demonstrated advantages over the other numerical methods. Results are reported to evaluate the influences of stiffeners with different angles and input factors on the nonlinear vibration, dynamic and static post-buckling (SPB) behaviors of FG variable thickness TSSs reinforced with spiral stiffeners.

Pointed masonry barrel vaults are widely used in classical historic structures, such as cathedrals and aqueducts, and they are very sensitive to differential settlement. These vaults are assemblages of masonry units and mortar. Since the bonding strength of mortar degrades over ages, dry-joint assumption is widely accepted. Failure behavior of dry-joint pointed masonry barrel vaults subjected to differential settlement is highly complex, discontinuous, and nonlinear. In this study, a 3D GPGPU-parallelized hybrid finite-discrete element method (FDEM), which is an advanced extension of finite element method (FEM) and discrete element method (DEM), is employed to investigate the capacity of pointed masonry barrel vaults subjected to differential settlement. When modeling barrel vaults with 3D FDEM, each masonry unit is discretized into a couple of four-node tetrahedral elements whose deformability is characterized by standard finite element formulation. Thus, structural deformation and interaction forces can be obtained in an accurate manner. Numerical examples are presented and validated with results from literatures. A base case is selected, and the influence of embrace angle (β), sharpness (Sh), stockiness (St), and out-of-plane length (L) on the failure behavior is parametrically investigated. The larger the β or Sh, the smaller the ultimate settlement. The same applies to St in general, while an excessively large St results in small ultimate settlement due to sliding. The influence of L can be mitigated should it is large enough compared with the span. It is demonstrated that the 3D GPGPU-parallelized FDEM is a robust tool for analyzing the vulnerability of pointed masonry barrel vaults subjected to differential settlement.

This paper presents the formulation of a new efficient and conforming rectangular finite element for analysis of thin plates with any arbitrary variation of thickness along both edges. Shape functions of this new element are derived from multiplying shape functions of non-prismatic Euler–Bernoulli beam extracted from basic displacement functions. To provide C1 consistency along the edges of elements, twist is added to conventional degrees of freedom, namely deflection and slopes resulting in an element with 16 degrees of freedom. The proposed element is used to solve various static and dynamic problems, and it is seen that the convergence of a new formulation occurs with much fewer elements compared to existing finite elements as a direct result of considering the variation of geometry in the derivation of shape functions, which renders the formulation competitive in both exactness and economy.

This study proposes a pseudo-lower bound method for direct limit analysis of two-dimensional structures and safety evaluation based on isogeometric analysis integrated through Bézier extraction. The key idea in this approach is that the stress field is separated into two parts: fictitious elastic and residual, and then the equilibrium conditions are recast by the weak form. Being different from the displacement approach which employs the kinematic formulation, the approximations based on the stress field satisfy automatically volumetric locking phenomena. Dealing with optimization problems, a second-order cone programming, providing significant advantages of the conic representation for yield criteria, is employed. The examination of various numerical benchmark problems shows an efficient and reliable method for the proposed approach.