Archive of Applied Mechanics最新文献

There has been a considerable number of studies on the reflection and transmission of plane waves in anisotropic elastic half-spaces. However, the obtained formulas of the reflection and transmission coefficients are implicit, and the numbers of reflected and transmitted waves are undetermined. In this paper, the reflection of qP waves from an orthotropic elastic layer overlying an orthotropic elastic half-space is considered. It has been proved that an incident qP wave always creates two reflected waves, one qP wave and one qSV wave, and the reflection angle of the reflected qP wave is equal to the incident angle. Based on this fact, formulas for the reflection coefficients have been derived by using the transfer matrix method along with the effective boundary condition technique. It should be noted that, different from the previously obtained implicit formulas, these formulas are totally explicit functions of the incident angle, the (dimensionless) layer thickness and the material parameters of the half-space and the layer. Since the obtained formulas are totally explicit, they will be useful in various practical applications, especially in nondestructively evaluating the mechanical properties of deposited layers.

Studies of the mechanical response behavior of slate and the establishment of corresponding damage-ontological relationships are crucial for improving safety and avoiding disasters in construction projects. For the study reported in this paper, we first assumed that slate is a transverse isotropic body. Next, to characterize disparities in elastic characteristics between axial and radial orientations, we introduced five distinct elastic parameters for these two directions. Specifically, these parameters were Young’s modulus E₁, Poisson’s coefficient v₁ (associated with parallel bedding planes), Young’s modulus E₂, Poisson’s coefficient v₂, and shear modulus G₂ (associated with perpendicular bedding planes). We then established a statistical damage-evolution equation for transverse isotropic slate based on a lognormal distribution, and we constructed a statistical damage-constitutive model for laminated slate under three-way stress by considering the shear–slip deformation and closure deformation of the laminated surface. Finally, we demonstrated the effectiveness of our model by comparing its output data with results obtained in triaxial compression tests on slate. We found that the differential stress–strain curves obtained from the model and the tests were in good agreement in the peak front. Average relative errors of 15.62% and 16.19% were recorded for cases of 5 Mpa and 10 Mpa of enclosing pressure, respectively. The rationality of the established transverse isotropic slate damage-constitutive relationship was therefore proved.

In recent years, extensive studies on carbon nanotubes-reinforced composites (CNTRC) and graphene platelets-reinforced composites (GPLRC) have been conducted primarily within the framework of the classical elasticity or thermoelasticity. However, there lacks of researches on the thermoelastic behaviors of CNTRC/GPLRC structures based on the generalized thermoelasticity considering non-Fourier heat conduction, especially lacking of studies that address the microstructures of these materials incorporating nonlocal effects. To address this gap, this work applies the generalized thermoelastic theory, which incorporates dual-phase thermal relaxations, thermal nonlocality and elastic nonlocality, to investigating the thermoelastic vibration characteristics of a nanocomposite microbeam reinforced by both GPLs and CNTs. The Halpin–Tsai micromechanical model is used to evaluate the effective elastic modulus of the composite microbeam, which is then analyzed using the Euler–Bernoulli beam model and solved via Navier’s method to determine the natural frequency. In calculation, the unidirectional distribution and three different functionally graded (FG) distributions of CNTs and GPLs, i.e., FG-A, FG-X and FG-O and also the influences of the nonlocal parameters, the volume fraction indices and the mass fractions of GPLs and CNTs on the natural frequencies are examined. The obtained results show that FG-A type significantly influences the natural frequency. The inclusion of GPLs and CNTs in the epoxy resin matrix markedly increases the natural frequency of the microbeam, with hybrid reinforcement being superior to GPLRC and CNTRC. The nonlocal elasticity parameter negatively correlates with the natural frequency, while the mass fraction and volume fraction index of GPLs and CNTs positively correlate with the natural frequency.

In this paper, the multi-linear cohesive zone model has been extended to simulate the mixed-mode I/II delamination growth in composite laminates. In the extended multi-linear cohesive zone model, inclined spring elements have been used to consider the fracture process zone effects so that when the crack starts to grow, the spring stiffness changes based on the material’s traction–separation curve with any arbitrary shape of softening law. To apply mode II loading in addition to mode I, the angle of spring elements in each desired mixed-mode ratio has been calculated using analytical equations and applied in the finite element model. The simulation results as load–displacement curves at different mixed-mode ratios are compared with the available experimental results to investigate the validity and accuracy of the newly proposed model. The maximum load values in three different mixed-mode ratios have been well predicted with an average error of less than 6%. After that, the applicability of the extended multi-linear cohesive zone model is evaluated to estimate the mixed-mode I/II delamination R-curve behavior and an analytical relation for the R-curve is presented based on the spring elements’ energy. A good agreement has been obtained between the R-curves extracted by the new model and the available experimental R-curves. The results show that the extended multi-linear cohesive zone model in combination with the proposed analytical R-curve can accurately predict the mixed-mode I/II delamination growth in composite laminates by considering the effects of the fracture process zone.

Additive manufacturing (AM) offers new possibilities to fabricate and design lightweight lattice materials. Due to the superior mechanical properties of these lattice structures, they have the potential to replace honeycombs as cores in sandwich panels. In addition to the advantage of the integral fabrication thanks to AM, additively manufactured lattice core sandwich panels may be also used as heat exchangers, enabling a multifunctional use of the core. To ensure a reliable and safe structure, the mechanical response of lattice core sandwich panels under given load conditions must be predictable. In conventional sandwich panels subjected to compressive loads, the sandwich’s global buckling and the face sheets’ local buckling are the dominant failure modes. In constrast, core strut buckling may be the critical failure mode in lattice core sandwich panels. Therefore, an analytical 2D model to predict the local buckling of lattice core struts is considered in this study. Furthermore, the critical load for global buckling is obtained based on the first-order shear deformation theory. Thus, the transition from local buckling to global buckling depending on the length-to-thickness ratio is captured by the presented model. The comparison with finite element modeling of the sandwich model with truss cores has proved the accuracy of the derived model.

Multi-phase functionally graded materials (FGMs) have more design variables than their two-phase counterparts and thus provide larger space for tailoring effective properties to meet multifunctional requirements. Predicting response of structures to dynamic loading is essential for structural design. In this work, the size-dependent transient response of a sandwich microbeam under a moving mass is studied. The core of the microbeam is homogeneous, while the two face layers are made from a three-phase bidirectional FGM. Based on the quasi-3D theory and modified couple stress theory, differential equations of motion are derived and transferred to a discretized form using a finite element formulation. Dynamic response is evaluated for microbeam with different material distributions and sandwich configurations. Numerical result reveals that the influence of material distribution on the transient response is governed by the microstructural scale parameter, and this influence is less significant for the microbeam associated with a higher scale parameter. The effects of the material gradation, the scale parameter and the mass velocity on the transient behaviour are studied in detail. The effect of micromechanical models, namely the rule of mixture and the extended Mori–Tanaka scheme, used in estimating the effective moduli of the three-phase FGM is also examined and discussed.

This paper addresses the computational modeling of selective laser sintering (SLS) and 3D concrete printing (3DCP) processes in advanced manufacturing. We focus on the phenomena experienced by their feedstock materials at the level of their mesoscale (the sintering powder grain and concrete aggregate scales) during the manufacturing process. Our approach is based on the discrete element method (DEM) for representing the material’s mechanical behavior. In SLS, the DEM is then combined with a lumped heat transfer model for describing the powder particles’ thermal states when scanned by the laser beam. In 3DCP, in turn, the DEM is combined with the so-called discrete fresh concrete (DFC) model for representing the fresh concrete paste rheology. We then present a simple numerical solution scheme followed by numerical simulations on two model-problems, with which we illustrate the applicability of such modeling approach.

The article is devoted to the study of the influence of flexural deformation of the body of a freight wagon on the indicators of the interaction of rail fleet with rails. The considered indicators depend both on the design of the rail fleet, its condition and speed, and on the design and condition of the railroad track. A theoretical study was carried out using a model of spatial vibrations of a freight wagon as part of a homogeneous train. When carrying out calculations, the wagon body was considered as an absolutely rigid body and as a discrete multi-mass system with elastic connections between the masses. When choosing a design scheme, it was assumed that the wagon body is a deformable body and, when bending, has finite rigidity in the vertical and horizontal planes. As a result of the research, the dependences of the dynamic indicators of a freight wagon on the flexural deformation of the body and the speed of movement were obtained. Based on theoretical calculations, the influence of the deformability of the body on the interaction of rail fleet with the railroad track on a tangent level track and curved section with irregularities was assessed.

The increasing popularity of composites reinforced with fiber has spurred the development of sophisticated additive manufacturing technologies, allowing for precise tailoring of fiber orientation for optimization purposes. Despite significant advancements in fiber orientation optimization, the key challenge posed by stress yield criteria still needs to be solved. This work presents a novel optimization approach, aiming to minimize structural volume while incorporating local stress constraints based on the Tsai–Wu criterion. The proposed NDFO-adapt method optimizes material distribution, fiber angles, and the penalization field. This optimization process involves multiple design variables, and new schemes are introduced to determine these variables using an optimization algorithm and adaptive continuations based on the structural grayscale. Numerical examples show the effectiveness of the proposed method, providing valuable insights for optimizing fiber-reinforced materials considering stress constraints with potential applications in the design of lightweight, high-strength structures.

Wire arc additive manufacturing enables the production of components with high deposition rates and the incorporation of multiple materials. However, the manufactured components possess a wavy surface, which is a major difficulty when it comes to simulating the mechanical behavior of wire arc additively manufactured components and evaluation of experimental full-field measurements. In this work, the wavy surface of a thick-walled tube is measured with a portable 3D scanning technique first. Then, the surface contour is considered numerically using the finite cell method. There, hierarchic shape functions based on integrated Legendre polynomials are combined with a fictitious domain approach to simplify the discretization process. This enables a hierarchic p-refinement process to study the convergence of the reaction quantities and the surface strains under tension–torsion load. Throughout all considerations, uncertainties arising from multiple sources are assessed. This includes the material parameter identification, the geometry measurement, and the experimental analysis. When comparing experiment and numerical simulation, the in-plane surface strains are computed based on displacement data using radial basis functions as ansatz for global surface interpolation. It turns out that the finite cell method is a suitable numerical technique to consider the wavy surface encountered for additively manufactured components. The numerical results of the mechanical response of thick-walled tubes subjected to tension–torsion load demonstrate good agreement with real experimental data, particularly when employing higher-order polynomials. This agreement persists even under the consideration of the inherent uncertainties stemming from multiple sources, which are determined by Gaussian error propagation.